X684

CROSSDIFFERENCE OF X4 AND X32

X684 = perspector of hyperbola {A, B, C,X3,X511}}
< 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) { 114, 132 }: Central Line L(114, 132) { 122, 125 }: Central Line L(122, 125) { 110, 351 }: Central Line L(110, 351) { 325, 523 }: Central Line L(325, 523) { 520, 647 }: Central Line L(520, 647) { 147, 804 }: Central Line L(147, 804) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_685 = TRILINEAR POLE OF LINE X(4)X(98) (0.7921, 0.4572) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_122 = -OF-MEDIAL-TRIANGLE (0.5195, -0.0036) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_351 = CENTER OF THE PARRY CIRCLE (1.3537, 1.1619) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_804 = ODD (- 2, 2) INFINITY POINT (0.9171, 0.6474) X_684 = CROSSDIFFERENCE OF X(4) AND X(32) (-1.3586, -0.3494) A B C X685 X114 X132 X122 X125 X110 X351 X325 X523 X520 X647 X147 X804 X684 (a, b, c) = (5, 6, 7) | AB = 1

X684 (CROSSDIFFERENCE OF X4 AND X32) 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 \(f(A,B,C) = \sec B \sin^{3} C - \sec C \sin^{3} B\)
Search Value (6, 9, 13): \(29.602152635288\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(b^{2} + c^{2} - a^{2})(b^{2} - c^{2})(a^{2}b^{2} + a^{2}c^{2} - b^{4} - c^{4}) : :\)

▸ Incident Central Lines8 lines

{110, 351}, {114, 132}, {122, 125}, {147, 804}, {325, 523}, {520, 647}, {669, 924}, {2491, 3569}

▸ Functional Relations8 relations