X3318

INCIRCLE TRANSFORM T(X603)

X3318 = reflection of X1359 in X1
< 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) { 1359, 1 }: Central Line L(1359, 1) { 11, 123 }: Central Line L(11, 123) { 55, 108 }: Central Line L(55, 108) { 56, 1295 }: Central Line L(56, 1295) { 944, 1317 }: Central Line L(944, 1317) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1359 = BRISSE TRANSFORM OF X(102) (0.5861, 0.4661) X_1 = INCENTER (0.5714, 0.2333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_944 = HOFSTADTER TRAPEZOID POINT (0.5306, 0.0708) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_3318 = INCIRCLE TRANSFORM T(X(603)) (0.5568, 0.0005) A B C X1359 X1 X11 X123 X55 X108 X56 X1295 X944 X1317 X3318 (a, b, c) = (5, 6, 7) | AB = 1

X3318 (INCIRCLE TRANSFORM T(X603)) 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 \(u : v : w\) = X603
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.254781131014\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b + c - a)(b - c)^{2}[a^{3} + a^{2}(b + c) - a(b + c)^{2} - (b + c)(b - c)^{2}]^{2} (E\). Danneels)

X3318 lies on the incircle.

▸ Incident Central Lines5 lines

{1, 1359}, {11, 123}, {55, 108}, {56, 1295}, {944, 1317}

▸ Functional Relations3 relations