X3237

INTERSECTION OF LINES X1X_256 and X3X_1673

< 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) { 1, 256 }: Central Line L(1, 256) { 3, 1673 }: Central Line L(3, 1673) { 6, 1672 }: Central Line L(6, 1672) { 55, 1671 }: Central Line L(55, 1671) { 56, 1670 }: Central Line L(56, 1670) { 1124, 1689 }: Central Line L(1124, 1689) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1671 = INVERSE-IN-BROCARD-CIRCLE OF X(1343) (0.5882, 0.2477) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X(1342) (0.4118, -0.0436) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_3237 = INTERSECTION OF LINES X(1)X(256) and X(3)X(1673) (0.5311, 0.1667) A B C X1 X256 X3 X1673 X6 X1672 X55 X1671 X56 X1670 X1124 X1689 X3237 (a, b, c) = (5, 6, 7) | AB = 1

X3237 (INTERSECTION OF LINES X1X_256 and X3X_1673) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1 + \cos(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.943013674223\)
▸ Incident Central Lines13 lines

{1, 256}, {3, 1673}, {6, 1672}, {55, 1671}, {56, 1670}, {371, 3236}, {372, 3235}, {1124, 1689}, {1335, 1690}, {1664, 1675}, {1665, 1674}, {2007, 3103}, {2008, 3102}