X1024

INTERSECTION OF LINES X6X_513 ANDX(9)X522

X1024 = crossdifference of every pair of points on line X241X518
< 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) { 6, 513 }: Central Line L(6, 513) { 9, 522 }: Central Line L(9, 522) { 55, 650 }: Central Line L(55, 650) { 57, 649 }: Central Line L(57, 649) { 333, 1021 }: Central Line L(333, 1021) { 673, 812 }: Central Line L(673, 812) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1025 = INTERSECTION OF LINES X(2)X(7) AND X(100)X(109) (1.0996, 1.0180) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_9 = MITTENPUNKT (0.5110, 0.1615) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_812 = ODD (- 1, 1) INFINITY POINT (0.1586, -0.2483) X_1024 = INTERSECTION OF LINES X(6)X(513) ANDX(9)X(522) (1.0370, 0.0294) A B C X1025 X6 X513 X9 X522 X55 X650 X57 X649 X333 X1021 X673 X812 X1024 (a, b, c) = (5, 6, 7) | AB = 1

X1024 (INTERSECTION OF LINES X6X_513 ANDX(9)X522) 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 \(f(a,b,c) = (b - c)(b + c - a)/[b^{2} + c^{2} - a(b + c)]\)
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): \(-1.577234698361\)
▸ Incident Central Lines6 lines

{6, 513}, {9, 522}, {55, 650}, {57, 649}, {333, 1021}, {673, 812}

▸ Functional Relations2 relations