X3319

INCIRCLE TRANSFORM T(X654)

X3319 = reflection of X3326 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) { 3326, 1 }: Central Line L(3326, 1) { 11, 515 }: Central Line L(11, 515) { 522, 1317 }: Central Line L(522, 1317) { 513, 1361 }: Central Line L(513, 1361) { 517, 1364 }: Central Line L(517, 1364) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3326 = INCIRCLE TRANSFORM T(X(909)) (0.3488, 0.1636) X_1 = INCENTER (0.5714, 0.2333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1361 = BRISSE TRANSFORM OF X(104) (0.5091, 0.4581) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1364 = BRISSE TRANSFORM OF X(108) (0.6338, 0.0085) X_3319 = INCIRCLE TRANSFORM T(X(654)) (0.7941, 0.3030) A B C X3326 X1 X11 X515 X522 X1317 X513 X1361 X517 X1364 X3319 (a, b, c) = (5, 6, 7) | AB = 1

X3319 (INCIRCLE TRANSFORM T(X654)) 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 \(u : v : w\) = X654
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.066441353945\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = [2a^{4} - 2a^{3}(b + c) - a^{2}(b^{2} - 4bc + c^{2}) + 2a(b + c)(b - c)^{2} - (b^{2} - c^{2})^{2}]^{2}/(b + c - a) (E\). Danneels)

X3319 lies on the incircle.

▸ Incident Central Lines8 lines

{1, 3326}, {11, 515}, {55, 2716}, {56, 2222}, {513, 1361}, {517, 1364}, {522, 1317}, {944, 2720}

▸ Functional Relations2 relations