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EF_|_AD wanted, angle bisectors, circumcircles related

Source: 2020 XXV All-Ukrainian Correspondence MO grades 5-12 p8

April 29, 2021
geometryperpendicularUkraine Correspondence

Problem Statement

Let ABCABC be an acute triangle, DD be the midpoint of BCBC. Bisectors of angles ADBADB and ADCADC intersect the circles circumscribed around the triangles ADBADB and ADCADC at points EE and FF, respectively. Prove that EF⊥ADEF\perp AD.
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