X2974

8th MACBEATH POINT

X2974 = reflection of X2971 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) { 2971, 5 }: Central Line L(2971, 5) { 3, 76 }: Central Line L(3, 76) { 131, 132 }: Central Line L(131, 132) { 25, 925 }: Central Line L(25, 925) { 2, 2970 }: Central Line L(2, 2970) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2971 = 5th MACBEATH POINT (0.7640, 0.2670) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_131 = INTERSECTION OF LINES X(3)X(125) AND X(4)X(135) (0.3098, 0.1823) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_925 = ANTICOMPLEMENT OF X(136) (0.0074, -0.0312) X_2 = CENTROID (0.5374, 0.2000) X_2970 = 4th MACBEATH POINT (0.7397, 0.1669) X_2974 = 8th MACBEATH POINT (0.3482, 0.2308) A B C X2971 X5 X3 X76 X131 X132 X25 X925 X2 X2970 X2974 (a, b, c) = (5, 6, 7) | AB = 1

X2974 (8th 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 \(f(a,b,c) = (b^{2}\cos^{2} C + c^{2}\cos^{2} B - bc \cos A)^{2}\cos A\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.531513647409\)
▸ Incident Central Lines6 lines

{2, 2970}, {3, 76}, {5, 2971}, {25, 925}, {131, 132}, {1368, 2972}

▸ Functional Relations2 relations