X3174

X7-CEVA CONJUGATE OF X9

X3174 = crosssum of X663 and X3020
< 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) { 9, 55 }: Central Line L(9, 55) { 1, 142 }: Central Line L(1, 142) { 78, 390 }: Central Line L(78, 390) { 40, 518 }: Central Line L(40, 518) { 100, 1445 }: Central Line L(100, 1445) { 936, 1001 }: Central Line L(936, 1001) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_40 = BEVAN POINT (0.4286, -0.0292) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1445 = -BETH CONJUGATE OF X(344) (0.6570, 0.3740) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_3174 = -CEVA CONJUGATE OF X(9) (0.7534, 0.3567) A B C X7 X9 X55 X1 X142 X78 X390 X40 X518 X100 X1445 X936 X1001 X3174 (a, b, c) = (5, 6, 7) | AB = 1

X3174 (X7-CEVA CONJUGATE OF X9) 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 \(x : y : z\) = X7 and \(u : v : w\) = X9
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): \(-6.518850176095\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines12 lines

{1, 142}, {9, 55}, {40, 518}, {65, 2136}, {78, 390}, {100, 1445}, {516, 1490}, {527, 2951}, {528, 1537}, {936, 1001}, {2324, 2340}, {2801, 2950}

▸ Functional Relations6 relations