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lines intersect at the circumcenter of the equilateral trapezoid

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1993 p3

February 20, 2020
geometryconcurrentIsosceles Trapezoidtrapezoidgeometric constructionconstruction

Problem Statement

Let AKLAKL be a triangle such that ∠ALK>90o+∠LAK\angle ALK > 90^o +\angle LAK. Construct an isosceles trapezoid ABCDABCD with AB∥CDAB \parallel CD such that KK lies on the side BC,LBC, L on the diagonal ACAC and the lines AKAK and BLBL intersect at the circumcenter of the trapezoid.
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