X1362

BRISSE TRANSFORM OF X105

X1362 = crosspoint of X7 and X241
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3041 }: Central Line L(2, 3041) { 43, 57 }: Central Line L(43, 57) { 12, 116 }: Central Line L(12, 116) { 11, 118 }: Central Line L(11, 118) { 56, 101 }: Central Line L(56, 101) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3041 = COMPLEMENT OF X(1362) (0.5857, 0.0866) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) A B C Ka Kb Kc X2 X3041 X43 X57 X12 X116 X11 X118 X56 X101 X1362 (a, b, c) = (5, 6, 7) | AB = 1

X1362 (BRISSE TRANSFORM OF X105) 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 = X105
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.445441009094\)

X1362 lies on the incircle.

▸ Incident Central Lines12 lines

{7, 1002}, {11, 118}, {12, 116}, {43, 57}, {55, 103}, {56, 101}, {59, 840}, {65, 1358}, {105, 651}, {150, 388}, {152, 497}, {928, 1361}

▸ Functional Relations9 relations