A circle through incenter
Posted: Sat Oct 25, 2014 5:04 pm
In $\Delta ABC$ , the incircle touches $AC,AB$ at the points $E,F$ respectively . $M$ is the midpoint of $EF$ . A circle $\omega$ (center $O$ ) is drawn through incenter $I$ and $M$ . Prove that $IO$ and $EF$ meet on the circle $\omega$ .
[edited. Thanks to Sowmitra .]
[edited. Thanks to Sowmitra .]