X3673

X3501com(INTOUCH TRIANGLE)

X3673 = complement of X25242
< 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) incircle: Incircle of △ABC { 4, 7 }: Central Line L(4, 7) { 10, 75 }: Central Line L(10, 75) { 1, 85 }: Central Line L(1, 85) { 2, 277 }: Central Line L(2, 277) { 158, 331 }: Central Line L(158, 331) { 315, 320 }: Central Line L(315, 320) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_2 = CENTROID (0.5374, 0.2000) X_277 = ISOGONAL CONJUGATE OF X(218) (0.4242, 0.1335) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_331 = ISOTOMIC CONJUGATE OF X(219) (0.6062, 0.4046) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_3673 = com(INTOUCH TRIANGLE) (0.5808, 0.2254) A B C X1 X4 X7 X10 X75 X85 X2 X277 X158 X331 X315 X320 X3673 (a, b, c) = (5, 6, 7) | AB = 1

X3673 (X3501com(INTOUCH 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 \(f(a,b,c) = bc(a^{2} + b^{2} + c^{2} - 2bc)\)
Search Value (6, 9, 13): \(1.857533642998\)
▸ Incident Central Lines19 lines

{1, 85}, {2, 277}, {3, 1447}, {4, 7}, {10, 75}, {20, 3598}, {77, 1067}, {150, 1837}, {158, 331}, {169, 673}, {274, 988}, {304, 350}, {312, 1930}, {315, 320}, {318, 1235}, {348, 3086}, {496, 1565}, {517, 3212}, {1434, 3338}

▸ Functional Relations2 relations