X2136

EIGENTRANSFORM OF X57

X2136 = X145-Ceva conjugate of X1
< 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) { 8, 9 }: Central Line L(8, 9) { 57, 145 }: Central Line L(57, 145) { 40, 376 }: Central Line L(40, 376) { 188, 258 }: Central Line L(188, 258) { 1, 474 }: Central Line L(1, 474) { 84, 952 }: Central Line L(84, 952) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1 = INCENTER (0.5714, 0.2333) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_40 = BEVAN POINT (0.4286, -0.0292) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_188 = 2nd MID-ARC POINT OF ANTICOMPLEMENTARY TRIANGLE (0.5245, 0.1802) X_258 = CONGRUENT INCIRCLES ISOSCELIZER POINT (0.5464, 0.1945) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_952 = INTERSECTION OF X(1)X(5) AND X(3)X(8) (0.1267, 0.6191) X_2136 = EIGENTRANSFORM OF X(57) (0.8750, 0.4082) A B C X145 X1 X8 X9 X57 X40 X376 X188 X258 X474 X84 X952 X2136 (a, b, c) = (5, 6, 7) | AB = 1

X2136 (EIGENTRANSFORM OF X57) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a (a^{2}+2 (b+c) a+b^{2}-6 b c+c^{2}) \cdot (-a+b+c) : :\)
Search Value (6, 9, 13): \(-12.846344671873\)

X2136 lies on the cubics K201 and K372.

▸ Incident Central Lines11 lines

{1, 474}, {8, 9}, {10, 1058}, {40, 376}, {43, 1050}, {57, 145}, {84, 952}, {100, 1420}, {188, 258}, {517, 1490}, {664, 738}

▸ Functional Relations8 relations