X3007

(DE LONGCHAMPS LINE)∩(SODDY LINE)

X3007 = crosspoint of X264 and X903
< 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) { 1, 7 }: Soddy Line { 325, 523 }: Central Line L(325, 523) { 5, 1441 }: Central Line L(5, 1441) { 953, 1305 }: Central Line L(953, 1305) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_903 = -BLAIKIE TRANSFORM OF X(2) (1.0000, 0.0000) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1441 = -BETH CONJUGATE OF X(313) (0.5459, 0.2242) X_953 = ISOGONAL CONJUGATE OF X(952) (0.0000, 0.2041) X_1305 = COLLINGS TRANSFORM OF X(440) (0.0205, -0.0724) X_3007 = (DE LONGCHAMPS LINE)∩(SODDY LINE) (0.0816, -0.8998) A B C X264 X903 X1 X7 X325 X523 X5 X1441 X953 X1305 X3007 (a, b, c) = (5, 6, 7) | AB = 1

X3007 ((DE LONGCHAMPS LINE)∩(SODDY LINE)) 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 \(f(a,b,c) = b^{3}(\sec^{2}(A/2) - \sec^{2}(B/2)) + c^{3}(\sec^{2}(A/2) - \sec^{2}(C/2))\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.120108754480\)
▸ Incident Central Lines4 lines

{1, 7}, {5, 1441}, {325, 523}, {953, 1305}

▸ Functional Relations5 relations