X629

COMPLEMENT OF X17

X629 is the complement of X17.
< 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) { 17, 627 }: Central Line L(17, 627) { 2, 17 }: Central Line L(2, 17) { 61, 302 }: Central Line L(61, 302) { 5, 618 }: Central Line L(5, 618) { 3, 623 }: Central Line L(3, 623) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_627 = ANTICOMPLEMENT OF X(17) (0.4791, 0.1233) X_2 = CENTROID (0.5374, 0.2000) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_618 = COMPLEMENT OF X(13) (0.5122, 0.1590) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_623 = COMPLEMENT OF X(15) (0.5302, 0.2060) X_629 = COMPLEMENT OF X(17) (0.5228, 0.1808) A B C X17 X627 X2 X61 X302 X5 X618 X3 X623 X629 (a, b, c) = (5, 6, 7) | AB = 1

X629 (COMPLEMENT OF X17) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [6S_{B}S_{C} + 7S_{A}a^{2} + 2 \sqrt{3} (b^{2} + c^{2}) \operatorname{area}]/a\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(3.250725913698\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(17)/a - \sec(A - \pi /3) : F(17)/b - \sec(B - \pi /3) : F(17)/c - \sec(C - \pi /3)\)

▸ Incident Central Lines6 lines

{2, 17}, {3, 623}, {5, 618}, {61, 302}, {140, 619}, {141, 575}

▸ Functional Relations4 relations