X1331

ORTHOCORRESPONDENT OF X101

For the definition of orthocorrespondent, see the notes just before X1992.
< 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) { 100, 109 }: Central Line L(100, 109) { 101, 110 }: Central Line L(101, 110) { 63, 212 }: Central Line L(63, 212) { 78, 255 }: Central Line L(78, 255) { 162, 190 }: Central Line L(162, 190) { 72, 283 }: Central Line L(72, 283) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) A B C X100 X109 X101 X110 X63 X212 X78 X255 X162 X190 X72 X283 X1331 (a, b, c) = (5, 6, 7) | AB = 1

X1331 (ORTHOCORRESPONDENT OF X101) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos A)/(b - c) : :\)
Search Value (6, 9, 13): \(-6.231052508554\)

X1331 lies on the MacBeath circumconic.

▸ Incident Central Lines14 lines

{63, 212}, {71, 895}, {72, 283}, {78, 255}, {100, 109}, {101, 110}, {145, 595}, {162, 190}, {228, 295}, {287, 293}, {394, 1260}, {677, 1252}, {901, 1293}, {906, 4574}

▸ Functional Relations9 relations