X3188

X27-CEVA CONJUGATE OF X7

X3188 = X27-Ceva conjugate of X7
< 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) { 1, 7 }: Soddy Line { 21, 85 }: Central Line L(21, 85) { 28, 272 }: Central Line L(28, 272) { 241, 379 }: Central Line L(241, 379) { 348, 377 }: Central Line L(348, 377) { 3, 1446 }: Central Line L(3, 1446) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_379 = EULER LINE INTERCEPT OF LINE X(6)X(7) (0.5733, 0.2937) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1446 = -BETH CONJUGATE OF X(349) (0.5951, 0.3031) X_3188 = -CEVA CONJUGATE OF X(7) (0.6701, 0.4616) A B C X27 X7 X1 X21 X85 X28 X272 X241 X379 X348 X377 X3 X1446 X3188 (a, b, c) = (5, 6, 7) | AB = 1

X3188 (X27-CEVA CONJUGATE OF X7) 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 \(x : y : z\) = X27 and \(u : v : w\) = X7
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-0.554702895498\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = [a^{5} - a^{4}(b + c) - a^{3}(b^{2} + c^{2}) + a^{2}(b^{3} + c^{3}) + bc(b + c)(b - c)^{2}]/(b + c - a) (E\). Danneels)

▸ Incident Central Lines9 lines

{1, 7}, {3, 1446}, {21, 85}, {28, 272}, {241, 379}, {348, 377}, {514, 1729}, {917, 934}, {958, 1441}

▸ Functional Relations1 relation