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fixed point wanted, point on circumcircle, reflection wrt angle bisector

Source: 2020 Dutch IMO TST 3.2

November 22, 2020
geometryreflectionFixed pointfixedcircumcircleangle bisector

Problem Statement

Given is a triangle ABCABC with its circumscribed circle and ∣AC∣<∣AB∣| AC | <| AB |. On the short arc ACAC, there is a variable point D≠AD\ne A. Let EE be the reflection of AA wrt the inner bisector of ∠BDC\angle BDC. Prove that the line DEDE passes through a fixed point, regardless of point DD.
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