X3050

INTERSECTION X6X_523∩X50X_647

X3050 = reflection of X6 in X3049
< 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) { 3049, 3288 }: Central Line L(3049, 3288) { 6, 523 }: Central Line L(6, 523) { 50, 647 }: Central Line L(50, 647) { 512, 1691 }: Central Line L(512, 1691) { 520, 2506 }: Central Line L(520, 2506) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3049 = INTERSECTION X(6)X(523)∩X(520)X(647) (2.6168, -0.5036) X_3288 = INTERSECTION OF LINES X(237)X(351) AND X(523)X(879) (6.6505, -2.0452) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.9991, 0.9263) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_2506 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE} (0.4241, 0.3737) X_3050 = INTERSECTION X(6)X(523)∩X(50)X(647) (4.6337, -1.2744) A B C X3049 X3288 X6 X523 X50 X647 X512 X1691 X520 X2506 X3050 (a, b, c) = (5, 6, 7) | AB = 1

X3050 (INTERSECTION X6X_523∩X50X_647) 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 \(f(a,b,c) = a(b^{2} - c^{2})(a^{4} - a^{2}b^{2} - a^{2}c^{2} - b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.549087959054\)
▸ Incident Central Lines5 lines

{6, 523}, {50, 647}, {512, 1691}, {520, 2506}, {669, 2513}

▸ Functional Relations6 relations