X1042

CROSSPOINT OF X1 AND X64

X1042 is the crosspoint of X1 and X64.
< 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) { 1, 7 }: Soddy Line { 31, 56 }: Central Line L(31, 56) { 42, 65 }: Central Line L(42, 65) { 34, 207 }: Central Line L(34, 207) { 57, 959 }: Central Line L(57, 959) { 241, 960 }: Central Line L(241, 960) 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_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_7 = GERGONNE POINT (0.5903, 0.2769) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_959 = ISOGONAL CONJUGATE OF X(958) (0.6111, 0.3031) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_1042 = CROSSPOINT OF X(1) AND X(64) (0.6427, 0.3981) A B C X1 X64 X7 X31 X56 X42 X65 X34 X207 X57 X959 X241 X960 X1042 (a, b, c) = (5, 6, 7) | AB = 1

X1042 (CROSSPOINT OF X1 AND X64) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (1 - \cos A)(\cos B + \cos C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(0.037415771731\)
▸ Incident Central Lines10 lines

{1, 7}, {31, 56}, {34, 207}, {42, 65}, {57, 959}, {241, 960}, {517, 1066}, {604, 608}, {741, 934}, {942, 1064}

▸ Functional Relations5 relations