X3040

COMPLEMENT OF X1361

X3040 is the complement of X1361.
< 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) { 8, 1364 }: Central Line L(8, 1364) { 109, 958 }: Central Line L(109, 958) { 2, 1361 }: Central Line L(2, 1361) { 124, 1329 }: Central Line L(124, 1329) { 102, 1376 }: Central Line L(102, 1376) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_1364 = BRISSE TRANSFORM OF X(108) (0.6338, 0.0085) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_2 = CENTROID (0.5374, 0.2000) X_1361 = BRISSE TRANSFORM OF X(104) (0.5091, 0.4581) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_3040 = COMPLEMENT OF X(1361) (0.5516, 0.0709) A B C X8 X1364 X109 X958 X2 X1361 X124 X1329 X102 X1376 X3040 (a, b, c) = (5, 6, 7) | AB = 1

X3040 (COMPLEMENT OF X1361) 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 \(f(a,b,c) = bc[b^{2}(1 - \cos A - \cos C)^{2}/(a - b + c) + c^{2}(1 - \cos A - \cos B)^{2}/(a + b - c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.853478619135\)

X3040 lies on the Spieker circle.

▸ Incident Central Lines12 lines

{2, 1361}, {8, 1364}, {10, 2818}, {102, 1376}, {109, 958}, {117, 2886}, {124, 1329}, {151, 2550}, {928, 3041}, {956, 1795}, {960, 2800}, {2835, 3039}

▸ Functional Relations3 relations