Table X-P
External Division.
Points available at the Kimberling's Encyclopedia ETC.
The ETC version: The 8998 points version of 2015.
The "Discoverer" database version: October 2013.
Last update: 2016-01-01

      Kimberling Notation     Role  
  1     X(2) Centroid     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 4:1  
  2     X(4) Orthocenter     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 4:3  
  3     X(20) de Longchamps Point     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 3:2  
  4     X(20) de Longchamps Point     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 4:3  
  5     X(20) de Longchamps Point     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 4:3  
  6     X(20) de Longchamps Point     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:8  
  7     X(140) Nine-Point Center of the Medial Triangle     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 3:1  
  8     X(140) Nine-Point Center of the Medial Triangle     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:1  
  9     X(145) Nagel Point of the Anticomplementary Triangle     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 4:3  
  10     X(165) Centroid of the Excentral Triangle     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(3) Circumcenter in the Ratio of 4:1  
  11     X(193)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 4:3  
  12     X(376)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 4:1  
  13     X(376)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 5:2  
  14     X(376)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 5:4  
  15     X(376)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:5  
  16     X(381) Center of the Orthocentroidal Circle     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 4:1  
  17     X(382)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 3:2  
  18     X(382)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 4:3  
  19     X(382)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 5:3  
  20     X(382)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 6:5  
  21     X(546)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 3:1  
  22     X(546)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 5:3  
  23     X(546)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:5  
  24     X(547)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 5:1  
  25     X(547)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:1  
  26     X(548)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 3:1  
  27     X(548)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:1  
  28     X(548)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:3  
  29     X(548)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 7:3  
  30     X(548)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:7  
  31     X(549)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 5:1  
  32     X(549)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:2  
  33     X(550)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 3:1  
  34     X(550)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 3:2  
  35     X(550)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 5:3  
  36     X(550)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 6:5  
  37     X(550)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:5  
  38     X(551)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 5:1  
  39     X(576)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 3:1  
  40     X(631)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 6:1  
  41     X(631)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:3  
  42     X(631)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:4  
  43     X(632)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 6:1  
  44     X(632)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:2  
  45     X(650) Center of the Stevanovic Circle     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 8:7  
  46     X(667)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:2  
  47     X(1125)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:1  
  48     X(1656)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 6:1  
  49     X(1656)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 6:1  
  50     X(1657)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 3:2  
  51     X(1657)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 5:4  
  52     X(1657)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 6:5  
  53     X(1657)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 7:6  
  54     X(1657)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:7  
  55     X(1698)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 6:1  
  56     X(2487)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 3:2  
  57     X(2487)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 5:2  
  58     X(2487)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 5:3  
  59     X(3090)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  60     X(3090)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:2  
  61     X(3091)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 6:1  
  62     X(3091)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 8:3  
  63     X(3091)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:4  
  64     X(3098)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(3) Circumcenter in the Ratio of 3:1  
  65     X(3146)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 3:2  
  66     X(3146)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 4:3  
  67     X(3146)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 5:4  
  68     X(3146)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 6:5  
  69     X(3146)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:8  
  70     X(3241)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 4:1  
  71     X(3244)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 3:1  
  72     X(3244)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 5:3  
  73     X(3244)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:5  
  74     X(3522)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 6:1  
  75     X(3522)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 7:2  
  76     X(3522)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 8:3  
  77     X(3522)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:4  
  78     X(3523)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:2  
  79     X(3524)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 4:1  
  80     X(3524)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 7:4  
  81     X(3526)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:2  
  82     X(3528)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 8:1  
  83     X(3528)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 9:2  
  84     X(3529)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 4:3  
  85     X(3529)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 6:5  
  86     X(3529)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 7:6  
  87     X(3529)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:7  
  88     X(3530)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:3  
  89     X(3530)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:5  
  90     X(3534)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 3:2  
  91     X(3534)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:2  
  92     X(3534)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 5:3  
  93     X(3534)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 7:4  
  94     X(3534)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 7:6  
  95     X(3543)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:2  
  96     X(3543)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 5:4  
  97     X(3543)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 7:4  
  98     X(3543)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 8:7  
  99     X(3545)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 4:1  
  100     X(3545)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 5:2  
  101     X(3579)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(3) Circumcenter in the Ratio of 3:1  
  102     X(3616)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 6:1  
  103     X(3617)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:4  
  104     X(3619)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 9:2  
  105     X(3620)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 9:4  
  106     X(3621)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 3:2  
  107     X(3621)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 4:3  
  108     X(3621)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:8  
  109     X(3622)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:2  
  110     X(3623)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 6:1  
  111     X(3623)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 8:3  
  112     X(3623)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:4  
  113     X(3625)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 3:1  
  114     X(3625)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 7:3  
  115     X(3625)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:7  
  116     X(3626)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:5  
  117     X(3627)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 3:1  
  118     X(3627)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 3:2  
  119     X(3627)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 7:3  
  120     X(3627)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 7:6  
  121     X(3627)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:7  
  122     X(3628)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:1  
  123     X(3628)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:1  
  124     X(3629)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 5:3  
  125     X(3630)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 9:7  
  126     X(3631)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 9:5  
  127     X(3632)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 5:3  
  128     X(3632)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 6:5  
  129     X(3633)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 3:2  
  130     X(3633)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 7:6  
  131     X(3633)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:7  
  132     X(3634)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:1  
  133     X(3635)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 5:1  
  134     X(3635)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 7:3  
  135     X(3676)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 7:2  
  136     X(3763)     Point Dividing Externally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 6:1  
  137     X(3828)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 5:1  
  138     X(3830)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 3:1  
  139     X(3830)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 4:1  
  140     X(3830)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 4:3  
  141     X(3830)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 5:2  
  142     X(3830)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 6:5  
  143     X(3830)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:5  
  144     X(3839)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 7:4  
  145     X(3839)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 8:5  
  146     X(3843)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:3  
  147     X(3845)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 3:2  
  148     X(3845)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 5:2  
  149     X(3845)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 5:3  
  150     X(3850)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 5:1  
  151     X(3850)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 7:3  
  152     X(3851)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  153     X(3853)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 3:1  
  154     X(3853)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:1  
  155     X(3853)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 5:3  
  156     X(3857)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 9:2  
  157     X(3858)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 7:2  
  158     X(3860)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 9:5  
  159     X(3861)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 7:3  
  160     X(4361)     Point Dividing Externally the Directed Segment from X(7) Gergonne Point to the X(1) Incenter in the Ratio of 7:6  
  161     X(4521)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 7:2  
  162     X(4663)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(6) Symmedian Point in the Ratio of 3:1  
  163     X(4669)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 5:3  
  164     X(4677)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 3:1  
  165     X(4677)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 4:1  
  166     X(4677)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 4:3  
  167     X(4701)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 5:1  
  168     X(4745)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 7:3  
  169     X(4816)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 6:1  
  170     X(4885)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 4:3  
  171     X(4897)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 7:6  
  172     X(5032)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 4:1  
  173     X(5054)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 5:2  
  174     X(5054)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 7:1  
  175     X(5055)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 4:1  
  176     X(5059)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 6:5  
  177     X(5059)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:8  
  178     X(5066)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 3:1  
  179     X(5066)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 7:1  
  180     X(5066)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 7:3  
  181     X(5071)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 7:2  
  182     X(5073)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 4:3  
  183     X(5073)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 7:6  
  184     X(5073)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:7  
  185     X(5076)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 6:1  
  186     X(5076)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 7:2  
  187     X(5093)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 4:1  
  188     X(5097)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 5:1  
  189     X(5102)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 5:2  
  190     X(5587)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 4:1  
  191     X(5603)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(5) Nine-Point Center in the Ratio of 4:1  
  192     X(5731)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(3) Circumcenter in the Ratio of 4:1  
  193     X(5734)     Point Dividing Externally the Directed Segment from X(8) Nagel Point to the X(5) Nine-Point Center in the Ratio of 8:3  
  194     X(5817)     Point Dividing Externally the Directed Segment from X(7) Gergonne Point to the X(5) Nine-Point Center in the Ratio of 4:1  
  195     X(5881)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 4:3  
  196     X(5882)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(1) Incenter in the Ratio of 3:1  
  197     X(6144)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 7:6  
  198     X(6666)     Point Dividing Externally the Directed Segment from X(7) Gergonne Point to the X(2) Centroid in the Ratio of 9:1  
  199     X(7263)     Point Dividing Externally the Directed Segment from X(7) Gergonne Point to the X(1) Incenter in the Ratio of 7:5  
  200     X(7967)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(1) Incenter in the Ratio of 4:1  
  201     X(7982)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(1) Incenter in the Ratio of 3:2  
  202     X(7989)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  203     X(7991)     Point Dividing Externally the Directed Segment from X(1) Incenter to the X(3) Circumcenter in the Ratio of 4:3  
  204     X(8148)     Point Dividing Externally the Directed Segment from X(3) Circumcenter to the X(1) Incenter in the Ratio of 4:3  
  205     X(8236)     Point Dividing Externally the Directed Segment from X(7) Gergonne Point to the X(1) Incenter in the Ratio of 4:1  
  206     X(8550)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(6) Symmedian Point in the Ratio of 3:1  
  207     X(8584)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 3:1  
  208     X(8703)     Point Dividing Externally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 3:1  
  209     X(8703)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 4:1  
  210     X(8703)     Point Dividing Externally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 4:3  
  211     X(8703)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:1  
  212     X(8703)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 7:3  
  213     X(8703)     Point Dividing Externally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:4