X324

ISOTOMIC CONJUGATE OF X97

X324 is the isotomic conjugate of X97.
< 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) { 4, 52 }: Central Line L(4, 52) { 2, 216 }: Central Line L(2, 216) { 53, 311 }: Central Line L(53, 311) { 94, 275 }: Central Line L(94, 275) { 110, 436 }: Central Line L(110, 436) { 143, 565 }: Central Line L(143, 565) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_4 = ORTHOCENTER (0.6122, 0.3958) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_2 = CENTROID (0.5374, 0.2000) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_94 = ISOGONAL CONJUGATE OF X(50) (0.9069, -0.1331) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_436 = EULER X(48)-7th-SUBSTITUTION POINT (0.6027, 0.3709) X_143 = NINE-POINT CENTER OF ORTHIC TRIANGLE (0.6358, 0.3534) X_565 = INTERSECTION OF LINES X(49)X(93) AND X(143,324) (0.3278, 0.5134) X_324 = ISOTOMIC CONJUGATE OF X(97) (0.5855, 0.3796) A B C X264 X5 X4 X52 X2 X216 X53 X311 X94 X275 X110 X436 X143 X565 X324 (a, b, c) = (5, 6, 7) | AB = 1

X324 (ISOTOMIC CONJUGATE OF X97) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc \sec A \cos(B - C) : ca \sec B \cos(C - A) : ab \sec C \cos(A - B)\)
Barycentrics: \(\sec A \cos(B - C) : \sec B \cos(C - A) : \sec C \cos(A - B)\)
Search Value (6, 9, 13): \(-0.654638902857\)
▸ Incident Central Lines6 lines

{2, 216}, {4, 52}, {53, 311}, {94, 275}, {110, 436}, {143, 565}

▸ Functional Relations8 relations