X889

INTERSECTION OF LINES X99X_898 AND X190X_649

X889 = trilinear pole of line X2X668
< 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) { 190, 649 }: Central Line L(190, 649) { 513, 668 }: Central Line L(513, 668) { 99, 898 }: Central Line L(99, 898) { 350, 903 }: Central Line L(350, 903) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_890 = ISOGONAL CONJUGATE OF X(889) (1.0440, 1.3495) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_99 = STEINER POINT (0.1109, 0.4322) X_898 = ISOGONAL CONJUGATE OF X(891) (0.9234, -0.1828) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_903 = -BLAIKIE TRANSFORM OF X(2) (1.0000, 0.0000) X_889 = INTERSECTION OF LINES X(99)X(898) AND X(190)X(649) (0.8340, -0.1151) A B C X890 X190 X649 X513 X668 X99 X898 X350 X903 X889 (a, b, c) = (5, 6, 7) | AB = 1

X889 (INTERSECTION OF LINES X99X_898 AND X190X_649) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a^{2}u^{2} - bcvw)/[a^{2}u(bv - cw)] : :\), where \(u : v : w\) = X513
Barycentrics: \(b c/((b - c) (a b + a c - 2 b c)) : :\)
Search Value (6, 9, 13): \(2.749435946006\)

X889 lies on the Steiner circumellipse, the hyperbola {A, B, C,PU(41)}}j.

▸ Incident Central Lines4 lines

{99, 898}, {190, 649}, {350, 903}, {513, 668}

▸ Functional Relations4 relations