X3677

X2999com(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 { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 9, 38 }: Central Line L(9, 38) { 244, 612 }: Central Line L(244, 612) { 613, 2003 }: Central Line L(613, 2003) { 42, 3243 }: Central Line L(42, 3243) { 200, 3242 }: Central Line L(200, 3242) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_613 = INTERSECTION OF LINES X(1)X(6) AND X(56)X(511) (0.5474, 0.2047) X_2003 = ORTHOCORRESPONDENT OF X(36) (0.5923, 0.2428) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_3243 = REFLECTION OF X(9) IN X(1) (0.6319, 0.3051) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_3242 = REFLECTION OF X(6) IN X(1) (0.5429, 0.1994) X_3677 = com(INTOUCH TRIANGLE) (0.5631, 0.2181) A B C X1 X3 X9 X38 X244 X612 X613 X2003 X42 X3243 X200 X3242 X3677 (a, b, c) = (5, 6, 7) | AB = 1

X3677 (X2999com(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 \(f(a,b,c) = a(a^{2} + 3b^{2} + 3c^{2} - 2bc)\)
Search Value (6, 9, 13): \(1.931209958765\)
▸ Incident Central Lines10 lines

{1, 3}, {9, 38}, {42, 3243}, {200, 3242}, {244, 612}, {518, 2999}, {613, 2003}, {1401, 3056}, {1449, 3509}, {2191, 2983}