X3578

INTERSECTION OF LINES X2X_6 AND X8X_30

X3578 = X75-Ceva conjugate of X1125
< 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) { 2, 6 }: Centroid–Symmedian Line { 8, 30 }: Central Line L(8, 30) { 340, 445 }: Central Line L(340, 445) { 540, 1046 }: Central Line L(540, 1046) { 542, 1281 }: Central Line L(542, 1281) { 519, 2292 }: Central Line L(519, 2292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_8 = NAGEL POINT (0.4694, 0.1333) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_445 = EULER X(79)-10th-SUBSTITUTION POINT (0.5856, 0.3259) X_540 = DIRECTION OF VECTOR AX + BX + CX, where X = X(58) (0.9208, 0.6443) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_542 = DIRECTION OF VECTOR AX + BX + CX, where X = X(98) (0.1649, 0.6534) X_1281 = 3rd SHARYGIN POINT (0.3110, 0.3100) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_2292 = -ISOCONJUGATE OF X(1169) (0.5509, 0.2064) X_3578 = INTERSECTION OF LINES X(2)X(6) AND X(8)X(30) (0.4652, 0.1224) A B C X75 X1125 X2 X6 X8 X30 X340 X445 X540 X1046 X542 X1281 X519 X2292 X3578 (a, b, c) = (5, 6, 7) | AB = 1

X3578 (INTERSECTION OF LINES X2X_6 AND X8X_30) 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 \(f(a,b,c) = bc(2a + b + c)(a^{2} - b^{2} - c^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.719444400426\)
▸ Incident Central Lines7 lines

{2, 6}, {8, 30}, {319, 3219}, {340, 445}, {519, 2292}, {540, 1046}, {542, 1281}

▸ Functional Relations2 relations