X3235

INTERSECTION OF LINES X1X_32 and X3X_2007

< 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, 32 }: Central Line L(1, 32) { 55, 1688 }: Central Line L(55, 1688) { 56, 1687 }: Central Line L(56, 1687) { 3, 2007 }: Central Line L(3, 2007) { 6, 2008 }: Central Line L(6, 2008) { 1124, 1342 }: Central Line L(1124, 1342) 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1688 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE) (1.4224, 1.6255) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1687 = INSIMILICENTER(1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE) (0.5757, 0.2271) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_3235 = INTERSECTION OF LINES X(1)X(32) and X(3)X(2007) (0.5954, 0.2683) A B C X1 X32 X55 X1688 X56 X1687 X3 X2007 X6 X2008 X1124 X1342 X3235 (a, b, c) = (5, 6, 7) | AB = 1

X3235 (INTERSECTION OF LINES X1X_32 and X3X_2007) 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 \(f(A,B,C) = 1 + \sin(A - \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.171647707336\)
▸ Incident Central Lines7 lines

{1, 32}, {3, 2007}, {6, 2008}, {55, 1688}, {56, 1687}, {1124, 1342}, {1335, 1343}