X3714

X386com(EXTOUCH TRIANGLE)

X3714 = excentral-to-ABC barycentric image of X386
< 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) { 10, 37 }: Central Line L(10, 37) { 8, 210 }: Central Line L(8, 210) { 12, 306 }: Central Line L(12, 306) { 65, 321 }: Central Line L(65, 321) { 72, 1089 }: Central Line L(72, 1089) { 536, 986 }: Central Line L(536, 986) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_3714 = com(EXTOUCH TRIANGLE) (0.4560, 0.1256) A B C X10 X37 X8 X210 X12 X306 X65 X321 X72 X1089 X536 X986 X3714 (a, b, c) = (5, 6, 7) | AB = 1

X3714 (X386com(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 \(f(a,b,c) = (b + c)(b + c - a)(a^{2} + ab + ac + 2bc)\)
Search Value (6, 9, 13): \(4.786771840422\)
▸ Incident Central Lines11 lines

{4, 3416}, {8, 210}, {10, 37}, {12, 306}, {65, 321}, {72, 1089}, {318, 1859}, {536, 986}, {1220, 1999}, {1840, 1869}, {2292, 3175}

▸ Functional Relations1 relation

  • X3714 = excentral-to-ABC barycentric image of X386