2007 IMO Problems/Problem 2

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

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

2007 IMO (Problems) • Resources
Preceded by Problem 1	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 3
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2007 IMO Problems/Problem 2

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