X3665

X41com(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 { 7, 21 }: Central Line L(7, 21) { 12, 85 }: Central Line L(12, 85) { 226, 241 }: Central Line L(226, 241) { 279, 388 }: Central Line L(279, 388) { 65, 760 }: Central Line L(65, 760) { 5, 1111 }: Central Line L(5, 1111) 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_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_760 = EVEN (1, 4) INFINITY POINT (0.2055, -0.2840) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1111 = TRILINEAR SQUARE OF X(514) (0.7470, 0.0849) X_3665 = com(INTOUCH TRIANGLE) (0.5672, 0.2394) A B C X1 X7 X21 X12 X85 X226 X241 X279 X388 X65 X760 X5 X1111 X3665 (a, b, c) = (5, 6, 7) | AB = 1

X3665 (X41com(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 \(f(a,b,c) = (b^{2} + c^{2})/(b + c - a)\)
Search Value (6, 9, 13): \(1.302527473162\)
▸ Incident Central Lines13 lines

{1, 1565}, {5, 1111}, {7, 21}, {12, 85}, {57, 1759}, {65, 760}, {226, 241}, {269, 1038}, {279, 388}, {1086, 2275}, {1355, 1367}, {1441, 3264}, {3160, 3476}