X306

ISOTOMIC CONJUGATE OF X27

X306 is the isotomic conjugate of X27.
< 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, 2 }: Nagel Line { 63, 69 }: Central Line L(63, 69) { 92, 264 }: Central Line L(92, 264) { 287, 293 }: Central Line L(287, 293) { 304, 305 }: Central Line L(304, 305) { 72, 440 }: Central Line L(72, 440) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_293 = ISOGONAL CONJUGATE OF X(240) (0.7839, -0.0636) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_440 = COMPLEMENT OF X(27) (0.4970, 0.0943) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) A B C X27 X1 X2 X63 X69 X92 X264 X287 X293 X304 X305 X72 X440 X306 (a, b, c) = (5, 6, 7) | AB = 1

X306 (ISOTOMIC CONJUGATE OF X27) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b^{2}c^{2})(b + c)\cos A : (c^{2}a^{2})(c + a)\cos B : (a^{2}b^{2})(a + b)\cos C\)
Barycentrics: \(bc(b + c)\cos A : ca(c + a)\cos B : ab(a + b)\cos C\)
Search Value (6, 9, 13): \(5.909803441297\)
▸ Incident Central Lines11 lines

{1, 2}, {27, 1043}, {63, 69}, {72, 440}, {92, 264}, {209, 518}, {226, 321}, {253, 329}, {287, 293}, {304, 305}, {319, 333}

▸ Functional Relations12 relations