X630

COMPLEMENT OF X18

X630 is the complement of X18.
< 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) { 18, 628 }: Central Line L(18, 628) { 2, 18 }: Central Line L(2, 18) { 62, 303 }: Central Line L(62, 303) { 5, 619 }: Central Line L(5, 619) { 3, 624 }: Central Line L(3, 624) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_628 = ANTICOMPLEMENT OF X(18) (0.7255, 0.3365) X_2 = CENTROID (0.5374, 0.2000) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_303 = ISOTOMIC CONJUGATE OF 2nd NAPOLEON POINT (0.6079, 0.2757) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_619 = COMPLEMENT OF X(14) (0.3494, 0.3571) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_624 = COMPLEMENT OF X(16) (-0.1165, -0.8620) X_630 = COMPLEMENT OF X(18) (0.5844, 0.2341) A B C X18 X628 X2 X62 X303 X5 X619 X3 X624 X630 (a, b, c) = (5, 6, 7) | AB = 1

X630 (COMPLEMENT OF X18) 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): \(12.084390187622\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(18)/a + \sec(A + \pi /3) : F(18)/b + \sec(B + \pi /3) : F(18)/c + \sec(C + \pi /3)\)

▸ Incident Central Lines6 lines

{2, 18}, {3, 624}, {5, 619}, {62, 303}, {140, 618}, {141, 575}

▸ Functional Relations4 relations