X3250

INTERSECTION OF X37X_513 AND X187X_237

X3250 = reflection of X649 in X665
< 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) { 649, 665 }: Central Line L(649, 665) { 187, 237 }: Central Line L(187, 237) { 37, 513 }: Central Line L(37, 513) { 514, 661 }: Central Line L(514, 661) { 789, 795 }: Central Line L(789, 795) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_795 = o-(- 3, 3) CIRCUMCIRCLE POINT (0.9741, -0.0867) X_3250 = INTERSECTION OF X(37)X(513) AND X(187)X(237) (23.9159, -12.4993) A B C X649 X665 X187 X237 X37 X513 X514 X661 X789 X795 X3250 (a, b, c) = (5, 6, 7) | AB = 1

X3250 (INTERSECTION OF X37X_513 AND X187X_237) 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 \(f(a,b,c) = a(b^{3} - c^{3})\)
Search Value (6, 9, 13): \(-19.930705958899\)
▸ Incident Central Lines5 lines

{37, 513}, {187, 237}, {514, 661}, {789, 795}, {798, 795}

▸ Functional Relations10 relations

Notes

Let L be the line P(6)U(6) = X37X513. Let M be the trilinear polar of the cevapoint of PU(6), this point being X256. Let V = P(6)-Ceva conjugate of U(6) and W = U(6)-Ceva conjugate of P(6). The lines L, M, VW concur in X3250. (Randy Hutson, December 26, 2015)