X3203

X54-CEVA CONJUGATE OF X39

X3203 = crosspoint of X1342 and X1343
< 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) { 83, 110 }: Central Line L(83, 110) { 32, 184 }: Central Line L(32, 184) { 140, 141 }: Central Line L(140, 141) { 6, 3202 }: Central Line L(6, 3202) 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_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3202 = -CEVA CONJUGATE OF X(32) (0.5821, -0.1114) X_3203 = -CEVA CONJUGATE OF X(39) (0.5970, 0.2043) A B C X54 X39 X83 X110 X32 X184 X140 X141 X6 X3202 X3203 (a, b, c) = (5, 6, 7) | AB = 1

X3203 (X54-CEVA CONJUGATE OF X39) 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 \(u : v : w\) = X39
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(6.074010394347\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{3}(b^{2} + c^{2})(a^{4} - b^{2}c^{2} - c^{2}a^{2} - a^{2}b^{2}) (E\). Danneels)

▸ Incident Central Lines4 lines

{6, 3202}, {32, 184}, {83, 110}, {140, 141}

▸ Functional Relations2 relations