X1251

ISOGONAL CONJUGATE OF X1082

X1251 is the isogonal conjugate of X1082.
< 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, 15 }: Central Line L(1, 15) { 13, 80 }: Central Line L(13, 80) { 55, 199 }: Central Line L(55, 199) { 7, 559 }: Central Line L(7, 559) { 37, 1250 }: Central Line L(37, 1250) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1082 = POINT ALPHERATZ (0.5483, 0.1908) X_1 = INCENTER (0.5714, 0.2333) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_7 = GERGONNE POINT (0.5903, 0.2769) X_559 = (X(1),X(15))-ANSWER TO QUESTION A (0.5825, 0.2536) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1250 = ISOGONAL CONJUGATE OF X(1081) (0.5229, 0.1536) X_1251 = ISOGONAL CONJUGATE OF X(1082) (0.5908, 0.2784) A B C X1082 X1 X15 X13 X80 X55 X199 X7 X559 X37 X1250 X1251 (a, b, c) = (5, 6, 7) | AB = 1

X1251 (ISOGONAL CONJUGATE OF X1082) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1082
Search Value (6, 9, 13): \(0.096700240411\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin(A) \csc(A/2) \sec(A/2 + \pi /6)\)

  • Trilinears: \((\cos A/2) \csc(A/2 - \pi /3) : :\)

▸ Incident Central Lines5 lines

{1, 15}, {7, 559}, {13, 80}, {37, 1250}, {55, 199}

▸ Functional Relations1 relation