X3725

X312com(INCENTRAL 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) { 31, 48 }: Central Line L(31, 48) { 37, 42 }: Central Line L(37, 42) { 1, 333 }: Central Line L(1, 333) { 43, 312 }: Central Line L(43, 312) { 55, 869 }: Central Line L(55, 869) { 354, 1201 }: Central Line L(354, 1201) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1 = INCENTER (0.5714, 0.2333) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_354 = WEILL POINT (0.5823, 0.2533) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_3725 = com(INCENTRAL TRIANGLE) (0.6101, 0.2733) A B C X31 X48 X37 X42 X1 X333 X43 X312 X55 X869 X354 X1201 X3725 (a, b, c) = (5, 6, 7) | AB = 1

X3725 (X312com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3}(b + c)(b^{2} + c^{2} + ab + ac)\)
Search Value (6, 9, 13): \(0.827438893234\)
▸ Linear Combinations1 combination
▸ Incident Central Lines13 lines

{1, 333}, {31, 48}, {37, 42}, {43, 312}, {55, 869}, {63, 2274}, {213, 1402}, {228, 1918}, {354, 1201}, {758, 982}, {960, 1193}, {2294, 3290}, {2308, 3248}