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ABC right angle triangle: FK=BC

Source: RMO Hyderabad 2016 , P5

October 12, 2016
geometrycircumcirclegeometric transformationreflection

Problem Statement

Let ABCABC be a right angled triangle with ∠B=90∘\angle B=90^{\circ}. Let ADAD be the bisector of angle AA with DD on BCBC . Let the circumcircle of triangle ACDACD intersect ABAB again at EE; and let the circumcircle of triangle ABDABD intersect ACAC again at FF . Let KK be the reflection of EE in the line BCBC . Prove that FK=BCFK = BC.
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