X1412

X81-BETH CONJUGATE OF X81

X1412 = X1014-Ceva conjugate of X58
< 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) { 56, 58 }: Central Line L(56, 58) { 57, 77 }: Central Line L(57, 77) { 86, 226 }: Central Line L(86, 226) { 109, 741 }: Central Line L(109, 741) { 394, 579 }: Central Line L(394, 579) { 552, 553 }: Central Line L(552, 553) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_552 = POINT MAIA I (0.6112, 0.3127) X_553 = POINT MAIA II (0.5963, 0.2857) X_1412 = -BETH CONJUGATE OF X(81) (0.6374, 0.3603) A B C X81 X56 X58 X57 X77 X86 X226 X109 X741 X394 X579 X552 X553 X1412 (a, b, c) = (5, 6, 7) | AB = 1

X1412 (X81-BETH CONJUGATE OF X81) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/((b + c) (a - b - c)) : :\)
Search Value (6, 9, 13): \(0.130923139220\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X81

  • Trilinears: cot(angle BAACA) : : , where BA and CA are the touchpoints of the B- and C-excircles with line BC, resp.

▸ Incident Central Lines17 lines

{21, 1420}, {28, 1422}, {56, 58}, {57, 77}, {86, 226}, {109, 741}, {110, 1477}, {269, 1396}, {283, 951}, {394, 579}, {552, 553}, {572, 940}, {580, 1092}, {1171, 1400}, {1326, 1402}, {1333, 1407}, {1427, 1461}

▸ Functional Relations5 relations