X1027

INTERSECTION OF LINES X1X_514 AND X6X_513

X1027 = crossdifference of every pair of points on line X518X672
< 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) { 105, 106 }: Central Line L(105, 106) { 1, 514 }: Central Line L(1, 514) { 6, 513 }: Central Line L(6, 513) { 56, 667 }: Central Line L(56, 667) { 292, 659 }: Central Line L(292, 659) { 58, 1019 }: Central Line L(58, 1019) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1026 = INTERSECTION OF LINES X(1)X(2) AND X(100)X(101) (4.1429, 3.7326) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_1 = INCENTER (0.5714, 0.2333) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1019 = -CEVA CONJUGATE OF X(1) (-29.0952, 18.1962) X_1027 = INTERSECTION OF LINES X(1)X(514) AND X(6)X(513) (1.0130, 0.0424) A B C X1026 X105 X106 X1 X514 X6 X513 X56 X667 X292 X659 X58 X1019 X1027 (a, b, c) = (5, 6, 7) | AB = 1

X1027 (INTERSECTION OF LINES X1X_514 AND X6X_513) 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 \(f(a,b,c) = (b - c)/[b^{2} + c^{2} - a(b + c)]\)
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): \(-0.746369991189\)
▸ Incident Central Lines7 lines

{1, 514}, {6, 513}, {56, 667}, {58, 1019}, {105, 106}, {292, 659}, {666, 1026}

▸ Functional Relations4 relations