2010 IMO Problems/Problem 2

Problem

Given a triangle $ABC$ , with $I$ as its incenter and $\Gamma$ as its circumcircle, $AI$ intersects $\Gamma$ again at $D$ . Let $E$ be a point on arc $BDC$ , and $F$ a point on the segment $BC$ , such that $\angle BAF=\angle CAE< \frac12\angle BAC$ . If $G$ is the midpoint of $IF$ , prove that the intersection of lines $EI$ and $DG$ lies on $\Gamma$ .

Authors: Tai Wai Ming and Wang Chongli, Hong Kong

Solution

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2010 IMO (Problems) • Resources
Preceded by Problem 1	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 3
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2010 IMO Problems/Problem 2

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