X3707

X45com(EXTOUCH TRIANGLE)

X3707 = excentral-to-ABC barycentric image of X45
< 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) { 8, 9 }: Central Line L(8, 9) { 10, 44 }: Central Line L(10, 44) { 72, 374 }: Central Line L(72, 374) { 142, 320 }: Central Line L(142, 320) { 45, 519 }: Central Line L(45, 519) { 333, 645 }: Central Line L(333, 645) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_374 = CENTROID OF THE PEDAL TRIANGLE OF X(9) (0.5449, 0.2238) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_645 = BARYCENTRIC MULTIPLIER FOR KIEPERT PARABOLA (-0.0375, 0.2992) X_3707 = com(EXTOUCH TRIANGLE) (0.4898, 0.1471) A B C X8 X9 X10 X44 X72 X374 X142 X320 X45 X519 X333 X645 X3707 (a, b, c) = (5, 6, 7) | AB = 1

X3707 (X45com(EXTOUCH 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 \(f(a,b,c) = (b + c - a)(4a + b + c)\)
Search Value (6, 9, 13): \(4.088483305504\)
▸ Incident Central Lines13 lines

{6, 1125}, {8, 9}, {10, 44}, {37, 3244}, {45, 519}, {72, 374}, {142, 320}, {210, 3271}, {226, 1405}, {333, 645}, {966, 1698}, {1449, 3622}, {3247, 3623}

▸ Functional Relations1 relation

  • X3707 = excentral-to-ABC barycentric image of X45