X3713

X2285com(EXTOUCH TRIANGLE)

X3713 = excentral-to-ABC barycentric image of X2285
< 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) { 6, 8 }: Central Line L(6, 8) { 9, 55 }: Central Line L(9, 55) { 37, 78 }: Central Line L(37, 78) { 220, 346 }: Central Line L(220, 346) { 572, 956 }: Central Line L(572, 956) { 72, 1766 }: Central Line L(72, 1766) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_572 = ORTHOGONAL OF X(58) (0.5253, 0.1439) X_956 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(8) (0.4790, 0.1235) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1766 = MIMOSA TRANSFORM OF X(345) (0.3896, -0.1193) X_3713 = com(EXTOUCH TRIANGLE) (0.4454, 0.1087) A B C X6 X8 X9 X55 X37 X78 X220 X346 X572 X956 X72 X1766 X3713 (a, b, c) = (5, 6, 7) | AB = 1

X3713 (X2285com(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 \(f(a,b,c) = a(b + c - a)^{2}(a^{2} + ab + ac + 2bc)\)
Search Value (6, 9, 13): \(4.826206501984\)
▸ Incident Central Lines11 lines

{6, 8}, {9, 55}, {37, 78}, {72, 1766}, {219, 2321}, {220, 346}, {518, 2285}, {572, 956}, {608, 1861}, {958, 2268}, {1376, 1400}

▸ Functional Relations1 relation

  • X3713 = excentral-to-ABC barycentric image of X2285