X1964

BICENTRIC SUM OF PU(36)

X1964 = crosssum of X1 and X75
< 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, 75 }: Central Line L(1, 75) { 31, 48 }: Central Line L(31, 48) { 6, 292 }: Central Line L(6, 292) { 82, 662 }: Central Line L(82, 662) { 99, 719 }: Central Line L(99, 719) { 110, 745 }: Central Line L(110, 745) 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_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_99 = STEINER POINT (0.1109, 0.4322) X_719 = EVEN (- 3, 1) CIRCUMCIRCLE POINT (1.0097, 0.1268) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_745 = EVEN (- 1, 3) CIRCUMCIRCLE POINT (0.9892, -0.0432) X_1964 = BICENTRIC SUM OF PU(36) (0.6058, 0.2641) A B C X1 X75 X31 X48 X6 X292 X82 X662 X99 X719 X110 X745 X1964 (a, b, c) = (5, 6, 7) | AB = 1

X1964 (BICENTRIC SUM OF PU(36)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{2}(b^{2} + c^{2}) : :\)
Search Value (6, 9, 13): \(0.925001725067\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(S_{A}\)\(S_{A}\) - \(S_{\omega }\)\(S_{\omega }\) : \(S_{B}\)\(S_{B}\) - \(S_{\omega }\)\(S_{\omega }\) : \(S_{C}\)\(S_{C}\) - \(S_{\omega }\)\(S_{\omega }\) (C. Lozada, 9/07/2013)

  • Trilinears: \(a^{2}(S_{A} + S_{\omega )} : :\) (C. Lozada, 9/07/2013)

  • Trilinears: \(\operatorname{area}(BCP(1)) + \operatorname{area}(BCU(1)) : :\)

▸ Incident Central Lines14 lines

{1, 75}, {6, 292}, {31, 48}, {42, 1100}, {82, 662}, {99, 719}, {110, 745}, {214, 995}, {313, 730}, {501, 595}, {741, 757}, {1042, 1360}, {1193, 1386}, {1201, 1279}

▸ Functional Relations8 relations