X3704

X58com(EXTOUCH TRIANGLE)

X3704 = excentral-to-ABC barycentric image of X58
< 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, 21 }: Central Line L(8, 21) { 10, 37 }: Central Line L(10, 37) { 12, 321 }: Central Line L(12, 321) { 65, 306 }: Central Line L(65, 306) { 141, 986 }: Central Line L(141, 986) { 40, 1503 }: Central Line L(40, 1503) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_40 = BEVAN POINT (0.4286, -0.0292) X_1503 = POINT ARKAB (0.4818, -0.3843) X_3704 = com(EXTOUCH TRIANGLE) (0.4421, 0.1132) A B C X8 X21 X10 X37 X12 X321 X65 X306 X141 X986 X40 X1503 X3704 (a, b, c) = (5, 6, 7) | AB = 1

X3704 (X58com(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 \(f(a,b,c) = (b + c)(b + c - a)(b^{2} + c^{2} + ab + ac)\)
Search Value (6, 9, 13): \(4.927281551674\)
▸ Incident Central Lines13 lines

{8, 21}, {10, 37}, {12, 321}, {40, 1503}, {65, 306}, {100, 1791}, {141, 986}, {197, 2915}, {312, 1329}, {346, 2551}, {524, 1046}, {960, 1682}, {1211, 2292}

▸ Functional Relations1 relation

  • X3704 = excentral-to-ABC barycentric image of X58