X3175

X7-CEVA CONJUGATE OF X10

X3175 = X7-Ceva conjugate of X10
< 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) { 2, 37 }: Central Line L(2, 37) { 72, 519 }: Central Line L(72, 519) { 428, 528 }: Central Line L(428, 528) { 354, 726 }: Central Line L(354, 726) { 190, 1999 }: Central Line L(190, 1999) { 1211, 2321 }: Central Line L(1211, 2321) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_354 = WEILL POINT (0.5823, 0.2533) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_1999 = ORTHOCORRESPONDENT OF X(10) (0.6884, 0.3479) X_1211 = ISOGONAL CONJUGATE OF X(1169) (0.5137, 0.1744) X_2321 = -ISOCONJUGATE OF X(1408) (0.4497, 0.1200) X_3175 = -CEVA CONJUGATE OF X(10) (0.7147, 0.3456) A B C X7 X10 X2 X37 X72 X519 X428 X528 X354 X726 X190 X1999 X1211 X2321 X3175 (a, b, c) = (5, 6, 7) | AB = 1

X3175 (X7-CEVA CONJUGATE OF X10) 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 \(f(a,b,c) = bc(b + c)(a^{2} + ab + ac - 2bc)\) (M. Iliev, 5/13/07)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b + c)(a^{2} + ab + ac - 2bc) (E\). Danneels)
Search Value (6, 9, 13): \(-2.719261742659\)
▸ Incident Central Lines6 lines

{2, 37}, {72, 519}, {190, 1999}, {354, 726}, {428, 528}, {1211, 2321}

▸ Functional Relations2 relations

  • X3175 = X7-Ceva conjugate of X10

  • X3175 = X2-of-inverse(n(Medial)*n(Incentral))-triangle