X3320

INCIRCLE TRANSFORM T(X656)

X3320 = X1297-of-Mandart-incircle-triangle
< 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) { 12, 127 }: Central Line L(12, 127) { 11, 132 }: Central Line L(11, 132) { 56, 112 }: Central Line L(56, 112) { 55, 1297 }: Central Line L(55, 1297) { 65, 1367 }: Central Line L(65, 1367) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1367 = BRISSE TRANSFORM OF X(112) (0.6451, 0.0119) X_3320 = INCIRCLE TRANSFORM T(X(656)) (0.5788, 0.4665) A B C X12 X127 X11 X132 X56 X112 X55 X1297 X65 X1367 X3320 (a, b, c) = (5, 6, 7) | AB = 1

X3320 (INCIRCLE TRANSFORM T(X656)) 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 \(u : v : w\) = X656
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.098781303603\)
▸ Alternate Coordinates1 form

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

X3320 lies on the incircle.

▸ Incident Central Lines5 lines

{11, 132}, {12, 127}, {55, 1297}, {56, 112}, {65, 1367}

▸ Functional Relations2 relations