Table X-P
Internal 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 Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 2:1  
  2     X(2) Centroid     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 2:1  
  3     X(2) Centroid     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 2:1  
  4     X(5) Nine-Point Center     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 3:1  
  5     X(10) Spieker Center     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 3:1  
  6     X(140) Nine-Point Center of the Medial Triangle     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 3:1  
  7     X(140) Nine-Point Center of the Medial Triangle     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 3:1  
  8     X(142) Mittenpunkt of the Medial Triangle     Point Dividing Internally the Directed Segment from X(7) Gergonne Point to the X(2) Centroid in the Ratio of 3:1  
  9     X(381) Center of the Orthocentroidal Circle     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 2:1  
  10     X(381) Center of the Orthocentroidal Circle     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 2:1  
  11     X(546)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 3:1  
  12     X(546)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 5:3  
  13     X(547)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 5:1  
  14     X(547)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 7:1  
  15     X(547)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:5  
  16     X(549)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 2:1  
  17     X(549)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:1  
  18     X(551)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 5:1  
  19     X(575)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 3:1  
  20     X(631)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 3:2  
  21     X(631)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 3:2  
  22     X(631)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 4:1  
  23     X(632)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 3:2  
  24     X(632)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:3  
  25     X(632)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:1  
  26     X(667)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 4:3  
  27     X(667)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 6:1  
  28     X(1125)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 3:1  
  29     X(1125)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 3:1  
  30     X(1656)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 3:2  
  31     X(1656)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 3:2  
  32     X(1656)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 4:1  
  33     X(1656)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:1  
  34     X(1698)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 3:2  
  35     X(1698)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:1  
  36     X(1699)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(4) Orthocenter in the Ratio of 2:1  
  37     X(3090)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 4:3  
  38     X(3090)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 4:3  
  39     X(3090)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 6:1  
  40     X(3090)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 6:1  
  41     X(3091)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 3:2  
  42     X(3091)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 3:2  
  43     X(3091)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 4:1  
  44     X(3523)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 4:3  
  45     X(3523)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 5:2  
  46     X(3523)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 6:1  
  47     X(3524)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 2:1  
  48     X(3524)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 7:2  
  49     X(3524)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 8:1  
  50     X(3525)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 6:5  
  51     X(3525)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 8:3  
  52     X(3525)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 9:2  
  53     X(3526)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 4:3  
  54     X(3526)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:2  
  55     X(3526)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 6:1  
  56     X(3530)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 3:1  
  57     X(3530)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(3) Circumcenter in the Ratio of 5:3  
  58     X(3530)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:1  
  59     X(3544)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 9:8  
  60     X(3545)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 2:1  
  61     X(3545)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:4  
  62     X(3545)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  63     X(3576)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(3) Circumcenter in the Ratio of 2:1  
  64     X(3589)     Point Dividing Internally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 3:1  
  65     X(3616)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 3:2  
  66     X(3616)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 4:1  
  67     X(3617)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 3:2  
  68     X(3617)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 3:2  
  69     X(3618)     Point Dividing Internally the Directed Segment from X(6) Symmedian Point to the X(2) Centroid in the Ratio of 3:2  
  70     X(3622)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 4:3  
  71     X(3622)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 6:1  
  72     X(3624)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 5:2  
  73     X(3624)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 6:1  
  74     X(3626)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 3:1  
  75     X(3626)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 5:3  
  76     X(3628)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 3:1  
  77     X(3628)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 3:1  
  78     X(3628)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:3  
  79     X(3634)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 5:3  
  80     X(3636)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 5:3  
  81     X(3636)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 7:1  
  82     X(3676)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(1) Incenter in the Ratio of 4:1  
  83     X(3679)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 2:1  
  84     X(3828)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 7:1  
  85     X(3828)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 7:5  
  86     X(3832)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 4:3  
  87     X(3832)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 4:3  
  88     X(3832)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:2  
  89     X(3839)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 2:1  
  90     X(3839)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 5:4  
  91     X(3839)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:2  
  92     X(3843)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 3:2  
  93     X(3843)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 4:1  
  94     X(3843)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 7:3  
  95     X(3845)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 2:1  
  96     X(3845)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 3:1  
  97     X(3845)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:1  
  98     X(3850)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 3:1  
  99     X(3850)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 5:3  
  100     X(3850)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:7  
  101     X(3851)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 4:3  
  102     X(3851)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 6:1  
  103     X(3851)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:5  
  104     X(3854)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:8  
  105     X(3855)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 6:5  
  106     X(3855)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:4  
  107     X(3855)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 8:3  
  108     X(3856)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:3  
  109     X(3857)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:2  
  110     X(3857)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 9:5  
  111     X(3858)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 3:2  
  112     X(3858)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:3  
  113     X(3859)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:3  
  114     X(3860)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 7:5  
  115     X(3860)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(4) Orthocenter in the Ratio of 9:7  
  116     X(3861)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(4) Orthocenter in the Ratio of 3:1  
  117     X(3861)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:1  
  118     X(4063)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 6:1  
  119     X(4468)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 4:1  
  120     X(4521)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 4:1  
  121     X(4521)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 8:7  
  122     X(4546)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 4:3  
  123     X(4668)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 4:1  
  124     X(4668)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 7:3  
  125     X(4669)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 3:1  
  126     X(4669)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 5:1  
  127     X(4678)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(8) Nagel Point in the Ratio of 4:3  
  128     X(4678)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 5:2  
  129     X(4691)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 5:3  
  130     X(4691)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 9:7  
  131     X(4745)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(2) Centroid in the Ratio of 5:3  
  132     X(4745)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 7:5  
  133     X(4746)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 7:1  
  134     X(4782)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(8) Nagel Point in the Ratio of 9:5  
  135     X(5050)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(6) Symmedian Point in the Ratio of 2:1  
  136     X(5054)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(2) Centroid in the Ratio of 2:1  
  137     X(5054)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(3) Circumcenter in the Ratio of 5:4  
  138     X(5054)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:2  
  139     X(5055)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 2:1  
  140     X(5055)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 5:1  
  141     X(5055)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 5:4  
  142     X(5055)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  143     X(5056)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 6:5  
  144     X(5056)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 8:3  
  145     X(5056)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:2  
  146     X(5066)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(5) Nine-Point Center in the Ratio of 5:1  
  147     X(5066)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 5:3  
  148     X(5066)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:5  
  149     X(5067)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 8:5  
  150     X(5067)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:4  
  151     X(5068)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 7:6  
  152     X(5068)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 9:4  
  153     X(5070)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:4  
  154     X(5070)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(5) Nine-Point Center in the Ratio of 8:3  
  155     X(5070)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:2  
  156     X(5071)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(5) Nine-Point Center in the Ratio of 4:1  
  157     X(5071)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(2) Centroid in the Ratio of 4:1  
  158     X(5071)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 8:7  
  159     X(5072)     Point Dividing Internally the Directed Segment from X(3) Circumcenter to the X(4) Orthocenter in the Ratio of 6:5  
  160     X(5079)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(3) Circumcenter in the Ratio of 7:6  
  161     X(5085)     Point Dividing Internally the Directed Segment from X(6) Symmedian Point to the X(3) Circumcenter in the Ratio of 2:1  
  162     X(5092)     Point Dividing Internally the Directed Segment from X(6) Symmedian Point to the X(3) Circumcenter in the Ratio of 3:1  
  163     X(5550)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(1) Incenter in the Ratio of 8:3  
  164     X(5550)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(2) Centroid in the Ratio of 9:2  
  165     X(5603)     Point Dividing Internally the Directed Segment from X(4) Orthocenter to the X(1) Incenter in the Ratio of 2:1  
  166     X(5657)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(3) Circumcenter in the Ratio of 2:1  
  167     X(5790)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(5) Nine-Point Center in the Ratio of 2:1  
  168     X(5818)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(5) Nine-Point Center in the Ratio of 4:1  
  169     X(5880)     Point Dividing Internally the Directed Segment from X(8) Nagel Point to the X(7) Gergonne Point in the Ratio of 3:1  
  170     X(5886)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 2:1  
  171     X(6329)     Point Dividing Internally the Directed Segment from X(2) Centroid to the X(6) Symmedian Point in the Ratio of 5:3  
  172     X(7486)     Point Dividing Internally the Directed Segment from X(5) Nine-Point Center to the X(2) Centroid in the Ratio of 9:8  
  173     X(7987)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(3) Circumcenter in the Ratio of 4:1  
  174     X(7988)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 8:1  
  175     X(8227)     Point Dividing Internally the Directed Segment from X(1) Incenter to the X(5) Nine-Point Center in the Ratio of 4:1