MathDB
Kazakhstan MO 2018

Source: Kazakhstan MO 2018 final round.Grade 11;Problem 1

May 4, 2018
geometryKazakhstan

Problem Statement

In an equilateral trapezoid, the point OO is the midpoint of the base ADAD. A circle with a center at a point OO and a radius BOBO is tangent to a straight line ABAB. Let the segment ACAC intersect this circle at point K(K≠C)K(K \ne C), and let MM is a point such that ABCMABCM is a parallelogram. The circumscribed circle of a triangle CMDCMD intersects the segment ACAC at a point L(L≠C)L(L\ne C). Prove that AK=CLAK=CL.
Back to ProblemsView on AoPS