X912

X104-CEVA CONJUGATE OF X3

As the isogonal conjugate of a point on the circumcircle, X912 lies on the line at infinity.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 3, 63 }: Central Line L(3, 63) { 1, 90 }: Central Line L(1, 90) { 65, 68 }: Central Line L(65, 68) { 5, 226 }: Central Line L(5, 226) { 30, 511 }: Central Line L(30, 511) { 38, 1064 }: Central Line L(38, 1064) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1064 = INTERSECTION OF LINES X(1)X(4) AND X(3)X(31) (0.5648, 0.2070) X_912 = -CEVA CONJUGATE OF X(3) (0.0031, -0.0428) A B C X104 X3 X63 X1 X90 X65 X68 X5 X226 X30 X511 X38 X1064 X912 (a, b, c) = (5, 6, 7) | AB = 1

X912 (X104-CEVA CONJUGATE OF X3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a^{2} - b^{2} - c^{2}) (a^{3} (b + c) - a^{2} (b^{2} + c^{2}) - a (b - c)^{2} (b + c) + (b^{2} - c^{2})^{2}) : :\)
▸ Incident Central Lines10 lines

{1, 90}, {3, 63}, {5, 226}, {30, 511}, {38, 1064}, {65, 68}, {222, 1060}, {601, 976}, {774, 1066}, {960, 993}

▸ Functional Relations6 relations