X3325

INCIRCLE TRANSFORM T(X896)

X3325 = X1296-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, 126 }: Central Line L(12, 126) { 56, 111 }: Central Line L(56, 111) { 55, 1296 }: Central Line L(55, 1296) { 65, 1366 }: Central Line L(65, 1366) 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_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_111 = PARRY POINT (0.9885, -0.0457) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1366 = BRISSE TRANSFORM OF X(111) (0.4238, 0.4139) X_3325 = INCIRCLE TRANSFORM T(X(896)) (0.7947, 0.1657) A B C X12 X126 X56 X111 X55 X1296 X65 X1366 X3325 (a, b, c) = (5, 6, 7) | AB = 1

X3325 (INCIRCLE TRANSFORM T(X896)) 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 \(u : v : w\) = X896
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.419671240495\)
▸ Alternate Coordinates1 form

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

X3325 lies on the incircle.

▸ Incident Central Lines4 lines

{12, 126}, {55, 1296}, {56, 111}, {65, 1366}

▸ Functional Relations2 relations