X191–X236

Ceva Conjugates

Perspectors of the cevian triangle of P and the anticevian triangle of Q (P-Ceva conjugates of Q) for classical triangle centers.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) ( A R_b ): Euclid I.22 Guide Circle (A) ( B R_a ): Euclid I.22 Guide Circle (B) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) circumcircle: Circumcircle of △ABC incircle: Incircle of △ABC A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) R_b = Radius Point R_b (0.8571, 0.0000) R_a = Radius Point R_a (0.2857, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1 = INCENTER (0.5714, 0.2333) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_197 = -CEVA CONJUGATE OF X(6) (0.4333, -0.1633) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_203 = -CEVA CONJUGATE OF X(16) (0.4136, 0.3918) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_224 = -CEVA CONJUGATE OF X(63) (1.2479, 0.4419) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) A B C X3 X1 X191 X192 X193 X194 X196 X197 X198 X203 X207 X208 X211 X222 X224 X230 X232 (a, b, c) = (5, 6, 7) | AB = 1

X191–X236 (Ceva Conjugates) — 15 representative centers (from 46 in collection) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Group Preamble — Centers X191-X236 (Ceva conjugates)

Centers X191-X236 are Ceva conjugates. (The P-Ceva conjugate of Q is the perspector of the cevian triangle of P and the anticevian triangle of Q.)

X_200 — X_8-CEVA CONJUGATE OF X_9

X200-CEVA CONJUGATE OF X9

X200 is the {X8,X78}-harmonic conjugate of X1. For a list of harmonic conjugates of X200, click Tables at the top of this page.
X_215 — X_1-CEVA CONJUGATE OF X_50

X215-CEVA CONJUGATE OF X50

X215 is the insimilicenter of the incircle and the sine-triple-angle circle. (Randy Hutson, December 14, 2014)