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EF tangent to circle (A,EB), <EAF=45^o, ABCD is square

Source: Netherlands - Dutch MO 1989 p2

December 25, 2022
squaretangentgeometry

Problem Statement

Given is a square ABCDABCD with E∈BCE \in BC, arbitrarily. On CDCD lies the point FF is such that ∠EAF=45o\angle EAF = 45^o. Prove that EFEF is tangent to the circle with center AA and radius ABAB.
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