X2991

DC(X105)

X2991 = reflection of X1332 in X6
< 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) { 1332, 6 }: Central Line L(1332, 6) { 6, 344 }: Central Line L(6, 344) { 294, 335 }: Central Line L(294, 335) { 193, 608 }: Central Line L(193, 608) { 31, 1331 }: Central Line L(31, 1331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1332 = ORTHOCORRESPONDENT OF X(100) (-0.2317, 0.1866) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_2991 = DC(X(105)) (1.4317, 0.3478) A B C X1332 X6 X344 X294 X335 X193 X608 X31 X1331 X2991 (a, b, c) = (5, 6, 7) | AB = 1

X2991 (DC(X105)) 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) is as given just before X2979, using U = X105
Search Value (6, 9, 13): \(41.697336848607\)

X2991 lies on the MacBeath circumconic.

▸ Incident Central Lines9 lines

{6, 344}, {31, 1331}, {110, 2203}, {193, 608}, {239, 1462}, {294, 335}, {604, 1445}, {918, 1814}, {1911, 2340}

▸ Functional Relations6 relations