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2018 JBMO TST- Macedonia, problem 2

Source: 2018 JBMO TST- Macedonia

May 28, 2019
JMMOJuniorMacedonia2018geometry

Problem Statement

We are given a semicircle kk with center OO and diameter ABAB. Let CC be a point on kk such that CO⊥ABCO \bot AB. The bisector of ∠ABC\angle ABC intersects kk at point DD. Let EE be a point on ABAB such that DE⊥ABDE \bot AB and let FF be the midpoint of CBCB. Prove that the quadrilateral EFCDEFCD is cyclic.
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