X750

INTERSECTION OF LINES X1X_88 AND X2X_31

X750 = isogonal conjugate of X751
< 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) { 2, 31 }: Central Line L(2, 31) { 1, 88 }: Central Line L(1, 88) { 38, 57 }: Central Line L(38, 57) { 43, 81 }: Central Line L(43, 81) { 5, 601 }: Central Line L(5, 601) { 12, 603 }: Central Line L(12, 603) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_751 = ISOGONAL CONJUGATE OF X(750) (0.5754, 0.2311) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) A B C X751 X2 X31 X1 X88 X38 X57 X43 X81 X5 X601 X12 X603 X750 (a, b, c) = (5, 6, 7) | AB = 1

X750 (INTERSECTION OF LINES X1X_88 AND X2X_31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2} + 2bc : b^{2} + 2ca : c^{2} + 2ab\)
Barycentrics: \(a^{3} + 2abc : b^{3} + 2abc : c^{3} + 2abc\)
Search Value (6, 9, 13): \(1.737657374421\)
▸ Incident Central Lines19 lines

{1, 88}, {2, 31}, {5, 601}, {6, 899}, {9, 896}, {12, 603}, {38, 57}, {42, 940}, {43, 81}, {46, 975}, {63, 756}, {140, 602}, {165, 968}, {255, 498}, {388, 1106}, {590, 606}, {605, 615}, {902, 1001}, {942, 976}

▸ Functional Relations1 relation