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intersection of circles is intersection of perpendicular bisectors

Source: 2020 Greek JBMO TST p1

November 14, 2020
geometryperpendicular bisectorconcurrencyconcurrent

Problem Statement

Let ABCABC be a triangle with AB>ACAB>AC. Let DD be a point on side ABAB such that BD=ACBD=AC. Consider the circle γ\gamma passing through point DD and tangent to side ACAC at point AA. Consider the circumscribed circle ω\omega of the triangle ABCABC that interesects the circle γ\gamma at points AA and EE. Prove that point EE is the intersection point of the perpendicular bisectors of line segments BCBC and ADAD.
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