Prove that OD is a the angle bisector of the angle BOC.

Question

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 $\angle BOC$.

Answer 1

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.

Answer 2

Thanks you for your solution. #Samara My solution: