X3252

INTERSECTION OF X7X_192 AND X37X_513

X3252 = X292-Ceva conjugate of X672
< 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) { 7, 192 }: Central Line L(7, 192) { 6, 292 }: Central Line L(6, 292) { 37, 513 }: Central Line L(37, 513) { 59, 604 }: Central Line L(59, 604) { 9, 660 }: Central Line L(9, 660) { 291, 1002 }: Central Line L(291, 1002) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_7 = GERGONNE POINT (0.5903, 0.2769) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_9 = MITTENPUNKT (0.5110, 0.1615) X_660 = TRILINEAR POLE OF LINE X(1)X(39) (0.9483, -0.0755) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_1002 = ISOGONAL CONJUGATE OF X(1001) (0.5967, 0.2704) X_3252 = INTERSECTION OF X(7)X(192) AND X(37)X(513) (35.2710, -18.6802) A B C X292 X672 X7 X192 X6 X37 X513 X59 X604 X9 X660 X291 X1002 X3252 (a, b, c) = (5, 6, 7) | AB = 1

X3252 (INTERSECTION OF X7X_192 AND X37X_513) 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 \(f(a,b,c) = a(b^{2} + c^{2} - ab - ac)/(a^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.550900416063\)
▸ Incident Central Lines8 lines

{6, 292}, {7, 192}, {9, 660}, {37, 513}, {59, 604}, {291, 1002}, {813, 840}, {984, 2113}

▸ Functional Relations2 relations