X741

EVEN (- 1, 1) CIRCUMCIRCLE POINT

X741 = Ψ(X190, X37)
< 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, 99 }: Central Line L(1, 99) { 42, 81 }: Central Line L(42, 81) { 31, 110 }: Central Line L(31, 110) { 58, 101 }: Central Line L(58, 101) { 86, 789 }: Central Line L(86, 789) { 21, 932 }: Central Line L(21, 932) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_1 = INCENTER (0.5714, 0.2333) X_99 = STEINER POINT (0.1109, 0.4322) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_932 = -CROSS CONJUGATE OF X(100) (0.0354, 0.3132) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) A B C X740 X1 X99 X42 X81 X31 X110 X58 X101 X86 X789 X21 X932 X741 (a, b, c) = (5, 6, 7) | AB = 1

X741 (EVEN (- 1, 1) CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = 1/[a ^{-2}(b^{1} + c^{1}) - a^{0}(b ^{-1} + c ^{-1})]\)
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): \(-0.106320646595\)

X741 lies on the circumcircle.

▸ Incident Central Lines14 lines

{1, 99}, {21, 932}, {31, 110}, {42, 81}, {58, 101}, {86, 789}, {107, 1096}, {334, 839}, {335, 835}, {689, 873}, {691, 923}, {759, 876}, {827, 849}, {934, 1042}

▸ Functional Relations10 relations