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Right triangle and ratio

Source: Sharygin contest. The final raund. 2008. Grade 8. First day. Problem 2

August 31, 2008
ratiotrigonometrygeometrycircumcirclegeometry unsolved

Problem Statement

(F.Nilov) Given right triangle ABC ABC with hypothenuse AC AC and \angle A \equal{} 50^{\circ}. Points K K and L L on the cathetus BC BC are such that \angle KAC \equal{} \angle LAB \equal{} 10^{\circ}. Determine the ratio CK/LB CK/LB.
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