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2010 IMO Problems/Problem 2

Revision as of 10:08, 20 July 2010 by Bugi (talk | contribs) (Created page with '== Problem == Given a triangle <math>ABC</math>, with <math>I</math> as its incenter and <math>\Gamma</math> as its circumcircle, <math>AI</math> intersects <math>\Gamma</math> …')
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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

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