X1354

BRISSE TRANSFORM OF X74

The following ten points lie on a circle: Xi for i = 11, 36, 65, 80, 108, 759, 1354, 1845, 2588, 2589. (Chris Van Tienhoven, Hyacinthos, January 4, 2011)
< 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) { 56, 759 }: Central Line L(56, 759) { 7, 1367 }: Central Line L(7, 1367) { 942, 1364 }: Central Line L(942, 1364) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1367 = BRISSE TRANSFORM OF X(112) (0.6451, 0.0119) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_1364 = BRISSE TRANSFORM OF X(108) (0.5367, 0.6071) X_1354 = BRISSE TRANSFORM OF X(74) (0.5512, 0.4657) A B C X56 X759 X7 X1367 X942 X1364 X1354 (a, b, c) = (5, 6, 7) | AB = 1

X1354 (BRISSE TRANSFORM OF X74) 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) is as above X1354, using X = X74
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.144941008250\)

X1354 lies on the incircle.

▸ Incident Central Lines3 lines

{7, 1367}, {56, 759}, {942, 1364}