X3326

INCIRCLE TRANSFORM T(X909)

X3326 = reflection of X3319 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) { 3319, 1 }: Central Line L(3319, 1) { 36, 1354 }: Central Line L(36, 1354) { 513, 1364 }: Central Line L(513, 1364) { 517, 1361 }: Central Line L(517, 1361) { 55, 2222 }: Central Line L(55, 2222) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3319 = INCIRCLE TRANSFORM T(X(654)) (0.7941, 0.3030) X_1 = INCENTER (0.5714, 0.2333) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1354 = BRISSE TRANSFORM OF X(74) (0.5512, 0.4657) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1364 = BRISSE TRANSFORM OF X(108) (0.6338, 0.0085) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1361 = BRISSE TRANSFORM OF X(104) (0.5091, 0.4581) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2222 = -ISOCONJUGATE OF X(654) (0.9870, 0.2545) X_3326 = INCIRCLE TRANSFORM T(X(909)) (0.3488, 0.1636) A B C X3319 X1 X36 X1354 X513 X1364 X517 X1361 X55 X2222 X3326 (a, b, c) = (5, 6, 7) | AB = 1

X3326 (INCIRCLE TRANSFORM T(X909)) 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 \(u : v : w\) = X909
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.314175664969\)
▸ Alternate Coordinates1 form

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

X3326 lies on the incircle.

▸ Incident Central Lines8 lines

{1, 3319}, {36, 1354}, {55, 2222}, {56, 2716}, {125, 2618}, {513, 1364}, {517, 1361}, {1118, 2745}

▸ Functional Relations2 relations