X3495

INTERSECTION OF LINES X32X_983 AND X39X_256

X3495 = isogonal conjugate of X3503
< 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) { 39, 256 }: Central Line L(39, 256) { 32, 983 }: Central Line L(32, 983) { 1, 3499 }: Central Line L(1, 3499) { 384, 3503 }: Central Line L(384, 3503) { 3498, 3501 }: Central Line L(3498, 3501) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3503 = ISOGONAL CONJUGATE OF X(3495) (0.6309, 0.3425) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_1 = INCENTER (0.5714, 0.2333) X_3499 = INTERSECTION OF LINES X(3)X(695) AND X(6)X(76) (0.6625, 0.3232) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_3498 = INTERSECTION OF LINES X(3)X(83) AND X(194)X(263) (0.6232, 0.3554) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) X_3495 = INTERSECTION OF LINES X(32)X(983) AND X(39)X(256) (0.4713, 0.1344) A B C X3503 X39 X256 X32 X983 X1 X3499 X384 X3498 X3501 X3495 (a, b, c) = (5, 6, 7) | AB = 1

X3495 (INTERSECTION OF LINES X32X_983 AND X39X_256) 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 \(f(a,b,c) = (b + c - a)/[b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2} - abc(b + c - a)] (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.307450989217\)

X3495 lies on the cubic Z(X384).

▸ Incident Central Lines5 lines

{1, 3499}, {32, 983}, {39, 256}, {384, 3503}, {3498, 3501}

▸ Functional Relations1 relation