X604

X56-CEVA CONJUGATE OF X31

X604 = isogonal conjugate of X312
< 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) { 6, 41 }: Central Line L(6, 41) { 57, 77 }: Central Line L(57, 77) { 31, 184 }: Central Line L(31, 184) { 1, 572 }: Central Line L(1, 572) { 36, 573 }: Central Line L(36, 573) { 109, 739 }: Central Line L(109, 739) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_1 = INCENTER (0.5714, 0.2333) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (1.0101, 0.0884) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) A B C X56 X31 X6 X41 X57 X77 X184 X1 X572 X36 X573 X109 X739 X604 (a, b, c) = (5, 6, 7) | AB = 1

X604 (X56-CEVA CONJUGATE OF X31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(1 - \cos A) : b(1 - \cos B) : c(1 - \cos C)\)
Barycentrics: \(a^{2}(1 - \cos A) : :\)
Search Value (6, 9, 13): \(0.089872087177\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(a^{2}(S_{A} - bc) : :\)

  • Trilinears: \(a^{2}/(b + c - a) : :\)

  • Trilinears: \(\operatorname{area}(A'BC) : :\), where A'B'C' = Fuhrmann triangle

  • Barycentrics: \(\sin^{2} A \sin^{2}(A/2) : :\)

▸ Incident Central Lines11 lines

{1, 572}, {6, 41}, {19, 909}, {31, 184}, {32, 1106}, {36, 573}, {57, 77}, {65, 1100}, {109, 739}, {219, 672}, {608, 1042}

▸ Functional Relations15 relations