Prove that OD is a the angle bisector of the angle BOC. Let $ABC$ be a non-isosceles triangle and $I$ be the intersection of the three internal angle bisectors. Let $D$ be a point of $BC$ such that $ID \perp BC$ and $O$ be a point on $AD$ such that $IO \perp AD$. 
Prove that $OD$ is a the angle bisector of $\angle BOC$.
This problem can be solve using the knowledge about Harmonic conjugate and polar. Notice me if you need those information. 


hope this still can help.
Thanks you for your solution. #Samara
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