X2971

5th MACBEATH POINT

X2971 = reflection of X2974 in X5
< 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) { 2974, 5 }: Central Line L(2974, 5) { 25, 111 }: Central Line L(25, 111) { 4, 147 }: Central Line L(4, 147) { 127, 136 }: Central Line L(127, 136) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2974 = 8th MACBEATH POINT (0.3482, 0.2308) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_111 = PARRY POINT (0.9885, -0.0457) X_4 = ORTHOCENTER (0.6122, 0.3958) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_136 = INTERSECTION OF LINE X(4)X(110) AND X(25)X(132) (0.8024, 0.3155) X_2971 = 5th MACBEATH POINT (0.7640, 0.2670) A B C X2974 X5 X25 X111 X4 X147 X127 X136 X2971 (a, b, c) = (5, 6, 7) | AB = 1

X2971 (5th MACBEATH POINT) 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 \(f(a,b,c) = [a(b^{2} - c^{2})]^{2}\cos B \cos C\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.637257130679\)
▸ Incident Central Lines4 lines

{4, 147}, {5, 2974}, {25, 111}, {127, 136}

▸ Functional Relations6 relations