X310

ISOTOMIC CONJUGATE OF X42

X310 is the isotomic conjugate of X42.
< 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, 39 }: Central Line L(2, 39) { 38, 75 }: Central Line L(38, 75) { 261, 272 }: Central Line L(261, 272) { 7, 314 }: Central Line L(7, 314) { 86, 350 }: Central Line L(86, 350) { 321, 335 }: Central Line L(321, 335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) X_7 = GERGONNE POINT (0.5903, 0.2769) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) A B C X42 X2 X39 X38 X75 X261 X272 X7 X314 X86 X350 X321 X335 X310 (a, b, c) = (5, 6, 7) | AB = 1

X310 (ISOTOMIC CONJUGATE OF X42) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{3}c^{3}/(b + c) : c^{3}a^{3}/(c + a) : a^{3}b^{3}/(a + b)\)
Barycentrics: \(b^{2}c^{2}/(b + c) : c^{2}a^{2}/(c + a) : a^{2}b^{2}/(a + b)\)
Search Value (6, 9, 13): \(4.317410031902\)
▸ Incident Central Lines10 lines

{2, 39}, {7, 314}, {38, 75}, {86, 350}, {99, 675}, {261, 272}, {321, 335}, {333, 673}, {670, 903}, {871, 982}

▸ Functional Relations9 relations