X3322

INCIRCLE TRANSFORM T(X665)

X3322 = reflection of X3328 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) { 3328, 1 }: Central Line L(3328, 1) { 7, 840 }: Central Line L(7, 840) { 56, 1308 }: Central Line L(56, 1308) { 516, 1155 }: Central Line L(516, 1155) { 514, 1317 }: Central Line L(514, 1317) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3328 = INCIRCLE TRANSFORM T(X(2291)) (0.3382, 0.2380) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0800, 0.3919) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1308 = COLLINGS TRANSFORM OF X(661) (1.0102, 0.0916) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1155 = SCHRÖDER POINT (1.7143, 2.3328) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_3322 = INCIRCLE TRANSFORM T(X(665)) (0.8047, 0.2285) A B C X3328 X1 X7 X840 X56 X1308 X516 X1155 X514 X1317 X3322 (a, b, c) = (5, 6, 7) | AB = 1

X3322 (INCIRCLE TRANSFORM T(X665)) 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 \(u : v : w\) = X665
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.000026128677\)
▸ Alternate Coordinates1 form

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

X3322 lies on the incircle.

▸ Incident Central Lines8 lines

{1, 3328}, {7, 840}, {55, 2222}, {56, 1308}, {513, 1362}, {514, 1317}, {516, 1155}, {1283, 1284}

▸ Functional Relations1 relation