X3245

REFLECTION OF X1 IN ITS TRILINEAR POLAR

X3245 is the reflection of X1 in its trilinear polar.
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 8, 535 }: Central Line L(8, 535) { 80, 516 }: Central Line L(80, 516) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_535 = DIRECTION OF VECTOR AX + BX + CX, where X = X(36) (0.8224, 0.7130) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_3245 = REFLECTION OF X(1) IN ITS TRILINEAR POLAR (2.8571, 4.4324) A B C X1 X3 X8 X535 X80 X516 X3245 (a, b, c) = (5, 6, 7) | AB = 1

X3245 (REFLECTION OF X1 IN ITS TRILINEAR POLAR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2b^{3} + 2c^{3} - a^{3} - 2(b + c)(a^{2} + bc) + a(b^{2} + c^{2} + 3bc) : :\)
Search Value (6, 9, 13): \(-11.106477378893\)
▸ Incident Central Lines3 lines

{1, 3}, {8, 535}, {80, 516}

▸ Functional Relations4 relations

  • X3245 = reflection of Xi in Xj for these (i,j): (1, 1155), (36, 484)

  • X3245 = X23-of-reflection-triangle-of-X1

  • X3245 = X10295-of-excentral-triangle

  • X3245 = endo-homothetic center of Ehrmann vertex-triangle and X2-Ehrmann triangle; the homothetic center is X7574