X2245

X2-ISOCONJUGATE OF X759

Let L denote the line having trilinears of X2245 as coefficients. Then L is the line passing through X1 perpendicular to the Euler line.
< 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) { 3, 6 }: Brocard Axis { 9, 46 }: Central Line L(9, 46) { 37, 65 }: Central Line L(37, 65) { 19, 407 }: Central Line L(19, 407) { 209, 228 }: Central Line L(209, 228) { 44, 513 }: Central Line L(44, 513) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_19 = CLAWSON POINT (0.6246, 0.4244) X_407 = CROSSPOINT OF X(4) AND X(225) (0.6211, 0.4189) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2245 = -ISOCONJUGATE OF X(759) (1.8169, 2.2770) A B C X3 X6 X9 X46 X37 X65 X19 X407 X209 X228 X44 X513 X2245 (a, b, c) = (5, 6, 7) | AB = 1

X2245 (X2-ISOCONJUGATE OF X759) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin A + \sin B + \sin C) \cos A - (\cos A + \cos B + \cos C) \sin A : :\)
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(-5.004425431428\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(\sin(A - B) + \sin(A - C) : :\)

  • Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X759

▸ Linear Combinations1 combination

  • X2245 = \(s\) X3 - \((r + R) \cot(\omega )\) X6

▸ Incident Central Lines22 lines

{3, 6}, {9, 46}, {19, 407}, {36, 2323}, {37, 65}, {40, 1834}, {44, 513}, {63, 1211}, {199, 2194}, {209, 228}, {219, 2178}, {377, 966}, {429, 1452}, {440, 1708}, {484, 2161}, {674, 2223}, {1100, 2260}, {1195, 2264}, {1405, 2267}, {1454, 2285}, {1631, 2175}, {1732, 2082}

▸ Functional Relations10 relations