X3041

COMPLEMENT OF X1362

X3041 is the complement of X1362.
< 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, 3022 }: Central Line L(8, 3022) { 118, 124 }: Central Line L(118, 124) { 101, 958 }: Central Line L(101, 958) { 9, 1282 }: Central Line L(9, 1282) { 2, 1362 }: Central Line L(2, 1362) 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_3022 = 6th STEVANOVIC POINT (0.7020, 0.0400) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1282 = 5th SHARYGIN POINT (-0.1429, 0.8165) X_2 = CENTROID (0.5374, 0.2000) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) X_3041 = COMPLEMENT OF X(1362) (0.5857, 0.0866) A B C X8 X3022 X118 X124 X101 X958 X9 X1282 X2 X1362 X3041 (a, b, c) = (5, 6, 7) | AB = 1

X3041 (COMPLEMENT OF X1362) 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 \(f(a,b,c) = bc[b^{2}(a^{2} - ab - bc + c^{2})^{2}/(a - b + c) + c^{2}(a^{2} - ac - bc + b^{2})^{2}/(a + b - c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.721332684186\)

X3041 lies on the Spieker circle.

▸ Incident Central Lines12 lines

{2, 1362}, {8, 3022}, {9, 1282}, {10, 2808}, {101, 958}, {103, 1376}, {118, 124}, {150, 2551}, {152, 2550}, {928, 3040}, {960, 2809}, {2801, 3035}

▸ Functional Relations2 relations