X3948

X3009com[INVERSE(n(INCENTRAL TRIANGLE))]

X3948 = isogonal conjugate of X18268
< 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) { 2, 39 }: Central Line L(2, 39) { 10, 321 }: Central Line L(10, 321) { 37, 313 }: Central Line L(37, 313) { 92, 429 }: Central Line L(92, 429) { 257, 312 }: Central Line L(257, 312) { 239, 350 }: Central Line L(239, 350) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_3948 = com[INVERSE(n(INCENTRAL TRIANGLE))] (-1.6430, -1.4511) A B C X2 X39 X10 X321 X37 X313 X92 X429 X257 X312 X239 X350 X3948 (a, b, c) = (5, 6, 7) | AB = 1

X3948 (X3009com[INVERSE(n(INCENTRAL 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 \(f(a,b,c) = bc(b + c)(bc - a^{2})\)
Search Value (6, 9, 13): \(14.830049694886\)
▸ Incident Central Lines21 lines

{1, 3765}, {2, 39}, {10, 321}, {37, 313}, {75, 1213}, {86, 3770}, {92, 429}, {190, 2245}, {192, 2092}, {239, 350}, {242, 862}, {257, 312}, {314, 1654}, {329, 2899}, {341, 1834}, {344, 1234}, {514, 661}, {536, 3264}, {714, 3122}, {730, 3009}, {1269, 3739}

▸ Functional Relations2 relations