X892

ISOGONAL CONJUGATE OF X351

X892 is the isogonal conjugate of X351.
< 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) { 111, 381 }: Central Line L(111, 381) { 99, 523 }: Central Line L(99, 523) { 316, 524 }: Central Line L(316, 524) { 670, 850 }: Central Line L(670, 850) { 805, 888 }: Central Line L(805, 888) { 880, 886 }: Central Line L(880, 886) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_351 = CENTER OF THE PARRY CIRCLE (1.3537, 1.1619) X_111 = PARRY POINT (0.9885, -0.0457) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_99 = STEINER POINT (0.1109, 0.4322) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (-0.0057, 0.2948) X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA (-6.8003, 1.7304) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_888 = ISOTOMIC CONJUGATE OF X(886) (0.2587, -0.3165) X_880 = INTERSECTION OF LINES X(6)X(76) AND X(99)X(670) (-2.0234, -2.0829) X_886 = INTERSECTION OF LINES X(99)X(669) AND X(512)X(670) (0.7371, -0.1549) X_892 = ISOGONAL CONJUGATE OF X(351) (1.0590, 0.0699) A B C X351 X111 X381 X99 X523 X316 X524 X670 X850 X805 X888 X880 X886 X892 (a, b, c) = (5, 6, 7) | AB = 1

X892 (ISOGONAL CONJUGATE OF X351) 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 \(u : v : w\) = X523
Search Value (6, 9, 13): \(-2.380234976912\)

X892 lies on the Steiner circumellipse.

▸ Incident Central Lines7 lines

{99, 523}, {111, 381}, {290, 895}, {316, 524}, {670, 850}, {805, 888}, {880, 886}

▸ Functional Relations7 relations

Notes

The osculating circle of the Steiner circumellipse at X99 intersects the Steiner circumellipse in two points: X99 and X892. See Osculating circle of Steiner circumellipse at X99. (Randy Hutson, November 5, 2021)