Construction of line knowing newton line direction
Source: AoPS
Given three lines a, b, c and two vectors u, v, construct a line d, with direction u, such that Newton line of the quadrilateral formed by the four lines a, b, c, d has direction v.
The three lines a, b, c form a triangle ABC. Let 𝒫 be the parabola inscribed in its medial triangle and whose axis has the direction of the vector u. Let d be the conjugate diameter of the direction of the vector v. 𝒫 and d intersects at a point Tuv. The tangent at Tuv to 𝒫 is Newton line of the quadrilateral abcd, which has the direction of the vector v.
Angel Montesdeoca. Enero, 2023