IMO Problem II

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October 26th 2010, 02:01 AM
simplependulum

IMO Problem II

This problem comes from this year's International Mathematical Olympiad , comparing with another geometry problem on the next day (problem 4) , this seems a little harder . Enjoy !

Let $I$ be the incentre of triangle $ABC$ and let $\Gamma$ be its circumcircle. Let the line $AI$ intersect $\Gamma$ again at $D$ . Let $E$ be a point on the arc $BDC$ and $F$ a point on the side $BC$ such that

$\angle BAF = \angle CAE < \frac{1}{2} \angle BAC$ .

Finally , let $G$ be the midpoint of the segment $IP$ . Prove that the lines $DG$ and $EI$ intersects on $\Gamma$ .
January 2nd 2011, 04:19 AM
BAdhi

sir, sorry for the late,late reply. now only i saw this thread

Quote:

Originally Posted by simplependulum

Finally , let $G$ be the midpoint of the segment $IP$ .

could you tell me what is $P$ here?
January 2nd 2011, 04:32 AM
Archie Meade

Quote:

Originally Posted by BAdhi

sir, sorry for the late,late reply. now only i saw this thread

could you tell me what is $P$ here?

In order that DG and EI intersect on the circumcircle,
G ought to be the midpoint of IF,
so I guess that's a typo.
January 2nd 2011, 05:30 AM
simplependulum

Yes , it is a typo . It should be $IF$ not $IP$ .