X3664

X37com(INTOUCH TRIANGLE)

X3664 = complement of X4416
< 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 { 10, 69 }: Central Line L(10, 69) { 58, 86 }: Central Line L(58, 86) { 6, 142 }: Central Line L(6, 142) { 222, 226 }: Central Line L(222, 226) { 255, 307 }: Central Line L(255, 307) 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_3664 = com(INTOUCH TRIANGLE) (0.5760, 0.2439) A B C X1 X7 X10 X69 X58 X86 X6 X142 X222 X226 X255 X307 X3664 (a, b, c) = (5, 6, 7) | AB = 1

X3664 (X37com(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 \(f(a,b,c) = 2a^{2} + a(b + c) - (b - c)^{2}\)
Search Value (6, 9, 13): \(1.488919677674\)
▸ Incident Central Lines22 lines

{1, 7}, {2, 1743}, {6, 142}, {10, 69}, {11, 1366}, {36, 1014}, {37, 527}, {57, 573}, {58, 86}, {75, 519}, {222, 226}, {255, 307}, {319, 3626}, {354, 1122}, {511, 942}, {948, 1419}, {1086, 1100}, {1099, 1111}, {1266, 3636}, {1394, 3485}, {1396, 1848}, {1565, 2792}

▸ Functional Relations1 relation

  • X3664 = complement of X4416