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largest possible area of the quadrilateral MKCL

Source: Czech-Polish-Slovak Junior Match 2016, individual p1 CPSJ

January 20, 2020
geometryareamaxperpendicular

Problem Statement

Let ABAB be a given segment and MM be its midpoint. We consider the set of right-angled triangles ABCABC with hypotenuses ABAB. Denote by DD the foot of the altitude from CC. Let KK and LL be feet of perpendiculars from DD to the legs BCBC and ACAC, respectively. Determine the largest possible area of the quadrilateral MKCLMKCL.
Czech Republic
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