MathDB
Parallelogram configuration with equal segments

Source: MEMO 2022 I3

September 2, 2022
geometry

Problem Statement

Let ABCDABCD be a parallelogram with ∠DAB<90\angle DAB < 90 Let EE be the point on the line BCBC such that AE=ABAE = AB and let FF be the point on the line CDCD such that AF=ADAF = AD. The circumcircle of the triangle CEFCEF intersects the line AEAE again in PP and the line AFAF again in QQ. Let XX be the reflection of PP over the line DEDE and YY the reflection of QQ over the line BFBF. Prove that A,X,YA, X, Y lie on the same line.
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