X2986

DC(X74)

X2986 = trilinear pole of line X3X523 (the line of the Ehrmann cross-triangle)
< 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) { 4, 110 }: Central Line L(4, 110) { 94, 323 }: Central Line L(94, 323) { 338, 394 }: Central Line L(338, 394) { 98, 858 }: Central Line L(98, 858) { 340, 687 }: Central Line L(340, 687) { 10, 1331 }: Central Line L(10, 1331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_94 = ISOGONAL CONJUGATE OF X(50) (0.9069, -0.1331) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_338 = CEVAPOINT OF X(115) AND X(125) (0.6941, 0.0587) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_98 = TARRY POINT (0.8891, -0.2281) X_858 = COMPLEMENT OF X(23) (0.1126, -0.9116) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_687 = TRILINEAR POLE OF LINE X(4)X(110) (1.3956, -3.1383) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_2986 = DC(X(74)) (1.2786, 0.1147) A B C X4 X110 X94 X323 X338 X394 X98 X858 X340 X687 X10 X1331 X2986 (a, b, c) = (5, 6, 7) | AB = 1

X2986 (DC(X74)) 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) is as given just before X2979, using U = X74
Barycentrics: \(1/(1 + \cos 2B + \cos 2C) : :\)
Search Value (6, 9, 13): \(3.913522972697\)

X2986 lies on the MacBeath circumconic.

▸ Incident Central Lines10 lines

{4, 110}, {10, 1331}, {94, 323}, {98, 858}, {226, 1813}, {262, 1995}, {321, 1332}, {338, 394}, {340, 687}, {648, 1993}

▸ Functional Relations6 relations

Notes

Let A'B'C' be the circumcevian triangle of X30. Let A″ be the trilinear pole of line B'C', and define B″, C″ cyclically. The lines AA″, BB″, CC″ concur in X2986. (Randy Hutson, June 27, 2018)