X1126

ISOGONAL CONJUGATE OF X1125

X1126 is the isogonal conjugate of X1125.
< 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) { 35, 42 }: Central Line L(35, 42) { 10, 86 }: Central Line L(10, 86) { 56, 181 }: Central Line L(56, 181) { 6, 595 }: Central Line L(6, 595) { 1, 748 }: Central Line L(1, 748) { 145, 996 }: Central Line L(145, 996) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_1 = INCENTER (0.5714, 0.2333) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_996 = INTERSECTION OF LINES X(8)X(58) AND X(10)X(56) (0.5332, 0.2018) X_1126 = ISOGONAL CONJUGATE OF X(1125) (0.5938, 0.2586) A B C X1125 X35 X42 X10 X86 X56 X181 X6 X595 X1 X748 X145 X996 X1126 (a, b, c) = (5, 6, 7) | AB = 1

X1126 (ISOGONAL CONJUGATE OF X1125) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/(2a+b+c) : b/(a+2b+c) : c/(a+b+2c)\)
Barycentrics: \(a^{2}/(2a+b+c) : b^{2}/(a+2b+c) : c^{2}/(a+b+2c)\)
Search Value (6, 9, 13): \(1.133263704558\)
▸ Incident Central Lines7 lines

{1, 748}, {6, 595}, {10, 86}, {35, 42}, {56, 181}, {145, 996}, {830, 1027}

▸ Functional Relations6 relations