CZ-SK-MO 1993 Problem 3

Let $AKL$ be a triangle such that $\angle ALK > 90^o +\angle LAK$ . Construct an isosceles trapezoid $ABCD$ with $AB \parallel CD$ such that $K$ lies on the side $BC, L$ on the diagonal $AC$ and the lines $AK$ and $BL$ intersect at the circumcenter of the trapezoid.