X3321

INCIRCLE TRANSFORM T(X663)

X3321 = crosspoint of X7 and X1323
< 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) { 7, 11 }: Central Line L(7, 11) { 55, 934 }: Central Line L(55, 934) { 57, 1358 }: Central Line L(57, 1358) { 1155, 1323 }: Central Line L(1155, 1323) { 1122, 1357 }: Central Line L(1122, 1357) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1323 = FLETCHER POINT (1.0262, 1.2854) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_1155 = SCHRÖDER POINT (1.7143, 2.3328) X_1122 = 1st GRINBERG POINT (0.6289, 0.3227) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) X_3321 = INCIRCLE TRANSFORM T(X(663)) (0.4744, 0.4455) A B C X7 X1323 X11 X55 X934 X57 X1358 X1155 X1122 X1357 X3321 (a, b, c) = (5, 6, 7) | AB = 1

X3321 (INCIRCLE TRANSFORM T(X663)) 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 \(f(a,b,c) = a(bw - cv)^{2}/(b + c - a) : b(cu - aw)^{2}/(c + a - b) : c(av - bu)^{2}/(a + b - c)\), where \(u : v : w\) = X663
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.294314075104\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = [2a^{2} - a(b + c) - (b - c)^{2}]^{2}/(b + c - a) (E\). Danneels)

X3321 lies on the incircle.

▸ Incident Central Lines5 lines

{7, 11}, {55, 934}, {57, 1358}, {1122, 1357}, {1155, 1323}

▸ Functional Relations3 relations