Consider a non-zero convex angle ∠POQ and its inner point M. Moreover, let m>0 be given. Construct a trapezoid ABCD satisfying the following conditions:
(1) vertices A,D lie on ray OP and vertices B,C lie on ray OQ,
(2) diagonals AC and BD intersect in M,
(3) AB=m.
Prove that your construction is correct and discuss conditions of solvability. geometryconstructive geometrytrapezoidnational olympiad