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2007 IMO Problems/Problem 2

Revision as of 00:11, 9 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Consider five points <math>A,B,C,D</math>, and <math>E</math> such that <math>ABCD</math> is a parallelogram and <math>BCED</math> is a cyclic quadrilateral. Let <...")
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Problem

Consider five points $A,B,C,D$, and $E$ such that $ABCD$ is a parallelogram and $BCED$ is a cyclic quadrilateral. Let $\ell$ be a line passing through $A$. Suppose that $\ell$ intersects the interior of the segment $DC$ at $F$ and intersects line $BC$ at $G$. Suppose also that $EF=EG=EC$. Prove that $\ell$ is the bisector of $\angle DAB$.

Solution

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