X3668

X219com(INTOUCH TRIANGLE)

X3668 = pole wrt polar circle of trilinear polar of X2322
< 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) incircle: Incircle of △ABC { 1, 7 }: Soddy Line { 19, 57 }: Central Line L(19, 57) { 37, 226 }: Central Line L(37, 226) { 10, 307 }: Central Line L(10, 307) { 142, 241 }: Central Line L(142, 241) { 158, 273 }: Central Line L(158, 273) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2328 = -ISOCONJUGATE OF X(1427) (0.5015, 0.1414) X_7 = GERGONNE POINT (0.5903, 0.2769) X_19 = CLAWSON POINT (0.6246, 0.4244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_3668 = com(INTOUCH TRIANGLE) (0.6162, 0.3370) A B C X1 X2328 X7 X19 X57 X37 X226 X10 X307 X142 X241 X158 X273 X3668 (a, b, c) = (5, 6, 7) | AB = 1

X3668 (X219com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos B + \cos C)/(1 + \cos A) : :\)
Barycentrics: \((b + c)/(b + c - a)^{2} : :\)
Search Value (6, 9, 13): \(0.168379201568\)
▸ Incident Central Lines28 lines

{1, 7}, {9, 948}, {10, 307}, {19, 57}, {37, 226}, {56, 2218}, {65, 1439}, {75, 1088}, {142, 241}, {158, 273}, {219, 527}, {222, 2219}, {342, 1785}, {387, 3339}, {534, 553}, {658, 897}, {759, 934}, {1020, 1400}, {1086, 1108}, {1122, 1358}, {1365, 2652}, {1367, 3324}, {1434, 2363}, {1445, 1723}, {1461, 1910}, {1486, 1617}, {2003, 2982}, {2217, 2385}

▸ Functional Relations4 relations

Notes

Let A'B'C' be the 3rd extouch triangle. Let A″ be the trilinear product B'*C', and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X3668. (Randy Hutson, September 14, 2016)

Let A13B13C13 be Gemini triangle 13. Let A' be the center of conic {{A, B, C,B13,C13}}, and define B' and C' cyclically. The lines AA', BB', CC' concur in X3668. (Randy Hutson, January 15, 2019)