X969

INTERSECTION OF LINES X10X_69 AND X19X_81

X969 = trilinear pole of line X661X905
< 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, 69 }: Central Line L(10, 69) { 19, 81 }: Central Line L(19, 81) { 37, 63 }: Central Line L(37, 63) { 65, 77 }: Central Line L(65, 77) { 7, 225 }: Central Line L(7, 225) { 158, 286 }: Central Line L(158, 286) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_968 = POINT ALDERAMIN (0.5557, 0.2126) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_19 = CLAWSON POINT (0.6246, 0.4244) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_7 = GERGONNE POINT (0.5903, 0.2769) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_969 = INTERSECTION OF LINES X(10)X(69) AND X(19)X(81) (0.5857, 0.2544) A B C X968 X10 X69 X19 X81 X37 X63 X65 X77 X7 X225 X158 X286 X969 (a, b, c) = (5, 6, 7) | AB = 1

X969 (INTERSECTION OF LINES X10X_69 AND X19X_81) 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 \(f(a,b,c) = 1/[a^{2} - 2a(b + c) - (b + c)^{2}]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.277232600254\)
▸ Incident Central Lines6 lines

{7, 225}, {10, 69}, {19, 81}, {37, 63}, {65, 77}, {158, 286}

▸ Functional Relations2 relations