X3674

X2329com(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, 7 }: Soddy Line { 76, 85 }: Central Line L(76, 85) { 57, 348 }: Central Line L(57, 348) { 65, 760 }: Central Line L(65, 760) { 552, 553 }: Central Line L(552, 553) { 274, 1432 }: Central Line L(274, 1432) 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_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_760 = EVEN (1, 4) INFINITY POINT (0.2055, -0.2840) X_552 = POINT MAIA I (0.6112, 0.3127) X_553 = POINT MAIA II (0.5963, 0.2857) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_1432 = -BETH CONJUGATE OF X(257) (0.6068, 0.2916) X_3674 = com(INTOUCH TRIANGLE) (0.5859, 0.2668) A B C X1 X7 X76 X85 X57 X348 X65 X760 X552 X553 X274 X1432 X3674 (a, b, c) = (5, 6, 7) | AB = 1

X3674 (X2329com(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 \(f(a,b,c) = (b^{2} + c^{2} + ab + ac)/(b + c - a)\)
Search Value (6, 9, 13): \(0.865977881421\)
▸ Incident Central Lines15 lines

{1, 7}, {10, 3212}, {57, 348}, {65, 760}, {76, 85}, {142, 3061}, {274, 1432}, {527, 2329}, {552, 553}, {942, 1565}, {1125, 1447}, {1358, 2795}, {1441, 1930}, {1446, 2051}, {3598, 3616}