Table X-P
Perspectors of the Fourth Brocard Triangle.
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: 2016-02-23

      Kimberling Notation     Role  
  1     X(2) Centroid     Perspector of the Fourth Brocard Triangle and Triangle ABC  
  2     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Medial Triangle  
  3     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Antimedial Triangle  
  4     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Half-Median Triangle  
  5     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Circum-Medial Triangle  
  6     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Symmedian Point in the Sidelines of the Anticevian Triangle of the Incenter  
  7     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Centroid in the Sidelines of the Pedal Triangle of the Symmedian Point  
  8     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Centroid in the Sidelines of the Antipedal Triangle of the Centroid  
  9     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Vertices of Triangle ABC in the Centroid  
  10     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Vertices of the Cevian Triangle of the Centroid in the Centroid  
  11     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Vertices of the Pedal Triangle of the Symmedian Point in the Symmedian Point  
  12     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Centroids of the Triangulation Triangles of the Centroid  
  13     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Inner Napoleon Points of the Pedal Corner Triangles of the First Isodynamic Point  
  14     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Outer Napoleon Points of the Pedal Corner Triangles of the Second Isodynamic Point  
  15     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Second Isodynamic Points of the Pedal Corner Triangles of the Outer Napoleon Point  
  16     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Inner Vecten Points of the Pedal Corner Triangles of the First Kenmotu Point  
  17     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Triangle of the Second Kenmotu Points of the Pedal Corner Triangles of the Outer Vecten Point  
  18     X(2) Centroid     Perspector and Homothetic Center of the Fourth Brocard Triangle and the Half-Circumcevian Triangle of the Centroid (Homothetic Triangles)  
  19     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Monge Triangle of the Incircles of the Triangulation Triangles of the Centroid  
  20     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Excircles and the Spieker Circle  
  21     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Mixtilinear Incircles and the Spieker Circle  
  22     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Lucas Circles and the Nine-Point Circle  
  23     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Lucas Circles and the Antimedial Circle  
  24     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Malfatti Circles and the Spieker Circle  
  25     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Inner Yff Circles and the Spieker Circle  
  26     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Outer Yff Circles and the Spieker Circle  
  27     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Excircles and the Spieker Circle of the Medial Triangle  
  28     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Excircles and the Incircle of the Antimedial Triangle  
  29     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Mixtilinear Incircles and the Spieker Circle of the Medial Triangle  
  30     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Mixtilinear Incircles and the Incircle of the Antimedial Triangle  
  31     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Lucas Circles and the Nine-Point Circle of the Medial Triangle  
  32     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Lucas Circles and the Antimedial Circle of the Antimedial Triangle  
  33     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Malfatti Circles and the Spieker Circle of the Medial Triangle  
  34     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Malfatti Circles and the Incircle of the Antimedial Triangle  
  35     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Johnson Circles and the Nine-Point Circle of the Medial Triangle  
  36     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Johnson Circles and the Antimedial Circle of the Antimedial Triangle  
  37     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Inner Yff Circles and the Incircle of the Antimedial Triangle  
  38     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Outer Yff Circles and the Incircle of the Antimedial Triangle  
  39     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Soddy Circles and the Orthocentroidal Circle of the Johnson Triangle  
  40     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Soddy Circles and the Orthocentroidal Circle of the Johnson Triangle  
  41     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Excircles and the Spieker Circle of the Half-Median Triangle  
  42     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Mixtilinear Incircles and the Spieker Circle of the Half-Median Triangle  
  43     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Soddy Circles and the Cosine Circle of the Honsberger Triangle  
  44     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Soddy Circles and the Cosine Circle of the Honsberger Triangle  
  45     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Lucas Circles and the Brocard Circle of the First Brocard Triangle  
  46     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Lucas Circles and the Nine-Point Circle of the Half-Median Triangle  
  47     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Malfatti Circles and the Spieker Circle of the Half-Median Triangle  
  48     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Johnson Circles and the Brocard Circle of the First Brocard Triangle  
  49     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the External Moses Triangle of the Johnson Circles and the Nine-Point Circle of the Half-Median Triangle  
  50     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Inner Yff Circles and the Spieker Circle of the Half-Median Triangle  
  51     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Outer Yff Circles and the Spieker Circle of the Half-Median Triangle  
  52     X(2) Centroid     Perspector of the Fourth Brocard Triangle and the Internal Moses Triangle of the Lucas Circles and the Johnson Circles  
  53     X(6) Symmedian Point     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Symmedian Point in the Sidelines of the Pedal Triangle of the Far-Out Point  
  54     X(6) Symmedian Point     Perspector of the Fourth Brocard Triangle and the Triangle of Reflections of the Vertices of the Anticevian Triangle of the Symmedian Point in the Euler Reflection Point  
  55     X(6) Symmedian Point     Perspector of the Fourth Brocard Triangle and the Triangle of the Euler Reflection Points of the Anticevian Corner Triangles of the Centroid  
  56     X(6) Symmedian Point     Perspector of the Fourth Brocard Triangle and the Triangle of the Centroids of the Anticevian Corner Triangles of the Parry Point  
  57     X(15) First Isodynamic Point     Perspector of the Fourth Brocard Triangle and the Outer Napoleon Triangle  
  58     X(15) First Isodynamic Point     Perspector of the Fourth Brocard Triangle and the Triangle of the Outer Napoleon Points of the Triangulation Triangles of the First Isodynamic Point  
  59     X(15) First Isodynamic Point     Perspector of the Fourth Brocard Triangle and the Stevanovic Triangle of the Outer Napoleon Points of the Triangulation Triangles of the First Isodynamic Point  
  60     X(16) Second Isodynamic Point     Perspector of the Fourth Brocard Triangle and the Inner Napoleon Triangle  
  61     X(61) Isogonal Conjugate of the Outer Napoleon Point     Perspector of the Fourth Brocard Triangle and the Stevanovic Triangle of the Nine-Point Centers of the Triangulation Triangles of the First Isodynamic Point  
  62     X(62) Isogonal Conjugate of the Inner Napoleon Point     Perspector of the Fourth Brocard Triangle and the Stevanovic Triangle of the Nine-Point Centers of the Triangulation Triangles of the Second Isodynamic Point  
  63     X(566)     Perspector of the Fourth Brocard Triangle and the Half-Antipedal Triangle of the Center of the Orthocentroidal Circle  
  64     X(8792)     Perspector of the Fourth Brocard Triangle and the Anticevian Triangle of the Perspector and Homothetic Center of the Orthic Triangle and the Tangential Triangle  
  65     X(8792)     Perspector of the Fourth Brocard Triangle and the Cevian Triangle of the Perspector of the Half-Symmedian Triangle and the Orthic Triangle  
  66     X(8877)     Perspector of the Fourth Brocard Triangle and the Anticevian Triangle of the Parry Point