X1795

INVERSE MIMOSA TRANSFORM OF X36

X1795 = trilinear pole of line X48X652
< 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) { 29, 58 }: Central Line L(29, 58) { 1, 104 }: Central Line L(1, 104) { 36, 102 }: Central Line L(36, 102) { 78, 255 }: Central Line L(78, 255) { 163, 284 }: Central Line L(163, 284) { 124, 499 }: Central Line L(124, 499) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1785 = MIMOSA TRANSFORM OF X(1295) (0.7297, 0.8635) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1 = INCENTER (0.5714, 0.2333) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_1795 = INVERSE MIMOSA TRANSFORM OF X(36) (0.7464, -0.0703) A B C X1785 X29 X58 X1 X104 X36 X102 X78 X255 X163 X284 X124 X499 X1795 (a, b, c) = (5, 6, 7) | AB = 1

X1795 (INVERSE MIMOSA TRANSFORM OF X36) 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 \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X36
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.141786694631\)
▸ Incident Central Lines16 lines

{1, 104}, {3, 1364}, {29, 58}, {35, 947}, {36, 102}, {56, 945}, {57, 1845}, {78, 255}, {117, 1478}, {124, 499}, {163, 284}, {171, 1065}, {219, 577}, {282, 1743}, {912, 1807}, {999, 1361}

▸ Functional Relations2 relations