X3202

X54-CEVA CONJUGATE OF X32

X3202 = X54-Ceva conjugate of X32
< 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) { 76, 110 }: Central Line L(76, 110) { 39, 184 }: Central Line L(39, 184) { 26, 206 }: Central Line L(26, 206) { 156, 2782 }: Central Line L(156, 2782) { 49, 3095 }: Central Line L(49, 3095) { 1916, 3044 }: Central Line L(1916, 3044) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE (0.1382, -0.8447) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_156 = -OF-TANGENTIAL-TRIANGLE (0.6520, -0.1707) X_2782 = ISOGONAL CONJUGATE OF X(2698) (0.9849, -0.1797) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_3095 = INTERSECTION OF LINES X(3)X(6) AND X(5)X(76) (0.6556, 0.3590) X_1916 = TRILINEAR POLE OF PU(11) (1.0447, 0.0288) X_3044 = INTERSECTION X(54)X(114)∩X(99)X(184) (0.8676, -0.0249) X_3202 = -CEVA CONJUGATE OF X(32) (0.5821, -0.1114) A B C X54 X32 X76 X110 X39 X184 X26 X206 X156 X2782 X49 X3095 X1916 X3044 X3202 (a, b, c) = (5, 6, 7) | AB = 1

X3202 (X54-CEVA CONJUGATE OF X32) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X54 and \(u : v : w\) = X32
Search Value (6, 9, 13): \(-0.467982044538\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{5}[a^{2}(b^{2} + c^{2}) - b^{4} - b^{2}c^{2} - c^{4}] (E\). Danneels)

▸ Incident Central Lines11 lines

{6, 3203}, {26, 206}, {39, 184}, {49, 3095}, {76, 110}, {156, 2782}, {1916, 3044}, {3104, 3201}, {3105, 3200}, {3106, 3206}, {3107, 3205}

▸ Functional Relations3 relations

Notes

Let A'B'C' be the triangle described in ADGEOM #2697 (8/26/2015, Tran Quang Hung). X3202 = X39-of-A'B'C'. (Randy Hutson, January 15, 2019)