X3696

X991com(EXTOUCH TRIANGLE)

X3696 = midpoint of X8 and X75
< 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, 75 }: Gergonne–Nagel Line { 7, 8 }: Gergonne–Nagel Line { 10, 37 }: Central Line L(10, 37) { 210, 321 }: Central Line L(210, 321) { 536, 984 }: Central Line L(536, 984) 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_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_3696 = com(EXTOUCH TRIANGLE) (0.4841, 0.1507) A B C X8 X75 X7 X10 X37 X210 X321 X536 X984 X3696 (a, b, c) = (5, 6, 7) | AB = 1

X3696 (X991com(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 \(f(a,b,c) = (b + c)(a^{2} - ab - ac - 2bc)\)
Search Value (6, 9, 13): \(4.106974490849\)
▸ Linear Combinations1 combination
▸ Incident Central Lines17 lines

{7, 8}, {10, 37}, {40, 1765}, {80, 2805}, {141, 1738}, {192, 3617}, {210, 321}, {239, 1386}, {318, 1882}, {536, 984}, {726, 3626}, {756, 3175}, {872, 3214}, {1150, 1155}, {1214, 2968}, {1376, 1402}, {1861, 1880}

▸ Functional Relations2 relations