MathDB
angle bisector wanted, # ABCD, cyclic BCED, EF = EG = EC

Source: Indonesia INAMO Shortlist 2017 G9 https://artofproblemsolving.com/community/c1101409_indonesia_shortlist__geometry

November 15, 2021
geometryangle bisectorcyclic quadrilateralparallelogramequal segments

Problem Statement

It is known that ABCDABCD is a parallelogram. The point EE is taken so that BCEDBCED is a cyclic quadrilateral. Let ℓ\ell be a line that passes through AA, intersects the segment DCDC at point FF and intersects the extension of the line BCBC at GG. Given EF=EG=ECEF = EG = EC. Prove that ℓ\ell is the bisector of the angle ∠BAD\angle BAD.
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