X3306

INTERSECTION OF LINES X1X_88 AND X2X_7

X3306 = crossdifference of every pair of points on the line X663X1635
< 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) { 2, 7 }: Centroid–Gergonne Line { 1, 88 }: Central Line L(1, 88) { 85, 658 }: Central Line L(85, 658) { 171, 614 }: Central Line L(171, 614) { 46, 1125 }: Central Line L(46, 1125) { 92, 1435 }: Central Line L(92, 1435) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1435 = -BETH CONJUGATE OF X(278) (0.6337, 0.5189) X_3306 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(7) (0.5633, 0.2377) A B C X2 X7 X1 X88 X85 X658 X171 X614 X46 X1125 X92 X1435 X3306 (a, b, c) = (5, 6, 7) | AB = 1

X3306 (INTERSECTION OF LINES X1X_88 AND X2X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((2 - \cos A) \csc A : (2 - \cos B) \csc B : (2 - \cos C) \csc C\)
Barycentrics: \(2 - \cos A : 2 - \cos B : 2 - \cos C\)
Search Value (6, 9, 13): \(1.794249868546\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc A + \tan(A/2) : :\)

▸ Incident Central Lines17 lines

{1, 88}, {2, 7}, {46, 1125}, {77, 1465}, {81, 2999}, {85, 658}, {92, 1435}, {145, 1706}, {165, 1621}, {171, 614}, {354, 1376}, {377, 1210}, {612, 982}, {748, 1707}, {940, 1100}, {1001, 1155}, {1038, 1393}

▸ Functional Relations5 relations