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max area of MKCE inscribed in square ABCD 1986 Kyiv City MO 10.5

Source:

July 16, 2021
geometrymaxgeometric inequalityareas

Problem Statement

Let EE be a point on the side ADAD of the square ABCDABCD. Find such points MM and KK on the sides ABAB and BCBC respectively, such that the segments MKMK and ECEC are parallel, and the quadrilateral MKCEMKCE has the largest area.
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