X575

ORTHOGONAL OF X187

X575 = Brocard-circle-invertse of X576
< 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) { 3, 6 }: Brocard Axis { 23, 51 }: Central Line L(23, 51) { 110, 373 }: Central Line L(110, 373) { 5, 542 }: Central Line L(5, 542) { 140, 524 }: Central Line L(140, 524) { 4, 598 }: Central Line L(4, 598) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_542 = DIRECTION OF VECTOR AX + BX + CX, where X = X(98) (0.1649, 0.6534) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_4 = ORTHOCENTER (0.6122, 0.3958) X_598 = ISOGONAL CONJUGATE OF X(574) (0.5865, 0.2783) X_575 = ORTHOGONAL OF X(187) (0.5750, 0.2259) A B C X3 X6 X23 X51 X110 X373 X5 X542 X140 X524 X4 X598 X575 (a, b, c) = (5, 6, 7) | AB = 1

X575 (ORTHOGONAL OF X187) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin A + \cot D/2 \cos A\), where \(\cot(D/2) = (a^{2} + b^{2} + c^{2})/(12 \operatorname{area})\)
Barycentrics: \(a^{2}(2a^{4} + b^{4} + c^{4} - 3a^{2}b^{2} - 3a^{2}c^{2} - 4b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(2.440272094848\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(3 \sin A + \cos A \cot \omega : :\) (Peter J. C. Moses, 7/20/03)

  • Trilinears: \(\cos A + 3 \sin A \tan \omega : :\) (Peter J. C. Moses, 8/22/03)

  • Trilinears: \(2 \cos(A - 2\omega ) - \cos(A + 2\omega ) + \cos A : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines8 lines

{3, 6}, {4, 598}, {5, 542}, {23, 51}, {54, 895}, {110, 373}, {140, 524}, {141, 629}

▸ Functional Relations7 relations