# Thread: IMO Problem II

1. ## 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 $\Gamma$ .

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

Originally Posted by simplependulum
Finally , let $G$ be the midpoint of the segment $IP$ .
could you tell me what is $P$ here?

3. 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.

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