X1237

ISOTOMIC CONJUGATE OF X1178

X1237 is the isotomic conjugate of X1178.
< 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) { 12, 313 }: Central Line L(12, 313) { 76, 334 }: Central Line L(76, 334) { 561, 756 }: Central Line L(561, 756) { 75, 1240 }: Central Line L(75, 1240) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1178 = 1st SARAGOSSA POINT OF X(82) (0.6029, 0.2656) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1240 = ISOTOMIC CONJUGATE OF X(1193) (0.4643, 0.1467) X_1237 = ISOTOMIC CONJUGATE OF X(1178) (0.4528, 0.1395) A B C X1178 X12 X313 X76 X334 X561 X756 X75 X1240 X1237 (a, b, c) = (5, 6, 7) | AB = 1

X1237 (ISOTOMIC CONJUGATE OF X1178) 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 \(f(a,b,c) = b^{3}c^{3}(b + c)(a^{2} + bc)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(4.897681688532\)
▸ Incident Central Lines4 lines

{12, 313}, {75, 1240}, {76, 334}, {561, 756}

▸ Functional Relations1 relation