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KL=LB, perpendiculars in right triangle (Kyiv City Olympiad 2006 8.3)

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June 28, 2020
geometryright triangleequal segmentsperpendicularllllllllllllllllllllllllllllll

Problem Statement

On the legs AC,BCAC, BC of a right triangle △ABC\vartriangle ABC select points MM and NN, respectively, so that ∠MBC=∠NAC\angle MBC = \angle NAC. The perpendiculars from points MM and CC on the line ANAN intersect ABAB at points KK and LL, respectively. Prove that KL=LBKL=LB.
(O. Clurman)
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