X748

INTERSECTION OF LINES X2X_31 AND X9X_38

X748 = isogonal conjugate of X749
< 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) { 9, 38 }: Central Line L(9, 38) { 11, 212 }: Central Line L(11, 212) { 63, 244 }: Central Line L(63, 244) { 44, 354 }: Central Line L(44, 354) { 181, 373 }: Central Line L(181, 373) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_749 = ISOGONAL CONJUGATE OF X(748) (0.6307, 0.4253) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_9 = MITTENPUNKT (0.5110, 0.1615) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_354 = WEILL POINT (0.5823, 0.2533) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) A B C X749 X2 X31 X9 X38 X11 X212 X63 X244 X44 X354 X181 X373 X748 (a, b, c) = (5, 6, 7) | AB = 1

X748 (INTERSECTION OF LINES X2X_31 AND X9X_38) 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): \(8.758009697598\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2} + rs - bcS :: b^{2} + rs - caS : c^{2} + rs - abS\)

▸ Incident Central Lines15 lines

{1, 756}, {2, 31}, {5, 602}, {9, 38}, {11, 212}, {21, 978}, {42, 1001}, {44, 354}, {55, 899}, {63, 244}, {140, 601}, {181, 373}, {255, 499}, {590, 605}, {606, 615}

▸ Functional Relations1 relation