X3982

X3683com(INTOUCH 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) incircle: Incircle of △ABC { 2, 7 }: Centroid–Gergonne Line { 382, 950 }: Central Line L(382, 950) { 546, 942 }: Central Line L(546, 942) { 1374, 1659 }: Central Line L(1374, 1659) { 1, 3529 }: Central Line L(1, 3529) { 65, 3626 }: Central Line L(65, 3626) 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_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_950 = CROSSPOINT OF X(8) AND X(29) (0.5621, 0.1961) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_1374 = 2nd GRIFFITHS POINT (0.5977, 0.2940) X_1659 = YIU-PAASCHE POINT (0.5749, 0.2470) X_3529 = EULER LINE INTERCEPT OF LINE X(516)X(944) (0.1633, -0.7790) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_3626 = H-1(X(1); M, -2) (0.4949, 0.1583) X_3982 = com(INTOUCH TRIANGLE) (0.5872, 0.2724) A B C X1 X2 X7 X382 X950 X546 X942 X1374 X1659 X3529 X65 X3626 X3982 (a, b, c) = (5, 6, 7) | AB = 1

X3982 (X3683com(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 \(f(a,b,c) = (a + b - c)(a - b + c)(2a + 3b + 3c)\)
Search Value (6, 9, 13): \(0.803227542353\)
▸ Incident Central Lines14 lines

{1, 3529}, {2, 7}, {65, 3626}, {382, 950}, {388, 3632}, {516, 3748}, {546, 942}, {554, 3639}, {1081, 3638}, {1319, 3636}, {1374, 1659}, {2099, 3244}, {3487, 3528}, {3664, 3782}