X2901

ORTHIC-ISOGONAL CONJUGATE OF X10

X2901 is the orthic-isogonal 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) { 10, 37 }: Central Line L(10, 37) { 1, 321 }: Central Line L(1, 321) { 72, 519 }: Central Line L(72, 519) { 312, 386 }: Central Line L(312, 386) { 346, 387 }: Central Line L(346, 387) { 354, 596 }: Central Line L(354, 596) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) X_354 = WEILL POINT (0.5823, 0.2533) X_596 = ISOGONAL CONJUGATE OF X(595) (0.4466, 0.1390) X_2901 = ORTHIC-ISOGONAL CONJUGATE OF X(10) (0.8536, 0.4818) A B C X4 X10 X37 X1 X321 X72 X519 X312 X386 X346 X387 X354 X596 X2901 (a, b, c) = (5, 6, 7) | AB = 1

X2901 (ORTHIC-ISOGONAL 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 \(f(a,b,c) = bc(b + c)(a^{3} + a^{2}b + a^{2}c - b^{2}c - bc^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-6.912928391241\)
▸ Incident Central Lines11 lines

{1, 321}, {10, 37}, {42, 1089}, {58, 1999}, {72, 519}, {312, 386}, {346, 387}, {354, 596}, {430, 1867}, {536, 942}, {1018, 2198}

▸ Functional Relations2 relations