X3531

INTERSECTION OF LINES X(3,373) AND X(69,381)

X3531 = perspector of circle (X3,2R)
< 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, 373 }: Central Line L(3, 373) { 69, 381 }: Central Line L(69, 381) { 399, 895 }: Central Line L(399, 895) { 54, 1598 }: Central Line L(54, 1598) { 74, 1597 }: Central Line L(74, 1597) { 25, 3431 }: Central Line L(25, 3431) 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_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_399 = PARRY REFLECTION POINT (0.0032, 0.9936) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_54 = KOSNITA POINT (0.5880, 0.2176) X_1598 = POINT CHERTAN II (0.6217, 0.4204) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_1597 = POINT CHERTAN I (0.6042, 0.3746) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_3431 = -VERTEX CONJUGATE OF X(6) (0.5702, 0.1746) X_3531 = INTERSECTION OF LINES X(3,373) AND X(69,381) (0.6096, 0.3476) A B C X3 X373 X69 X381 X399 X895 X54 X1598 X74 X1597 X25 X3431 X3531 (a, b, c) = (5, 6, 7) | AB = 1

X3531 (INTERSECTION OF LINES X(3,373) AND X(69,381)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(3 \cos A + \sin B \sin C) : :\)
Barycentrics: \(a^{2}/[7a^{4} - 8a^{2}(b^{2} + c^{2}) + (b^{2} - c^{2})^{2}] : :\)
Search Value (6, 9, 13): \(-2.524000026960\)

X3531 lies on the Jerabek hyperbola.

▸ Incident Central Lines7 lines

{3, 373}, {25, 3431}, {51, 3426}, {54, 1598}, {69, 381}, {74, 1597}, {399, 895}

▸ Functional Relations3 relations