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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 $\angle BOC$.

diagram

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  • $\begingroup$ Angle bisector of which angle? $\endgroup$ – user26486 Oct 22 '14 at 14:57
  • $\begingroup$ mathh: BOC. You, Kim Jong Un do it this problem, please. $\endgroup$ – Do Hoai Phuong Oct 22 '14 at 15:07
  • $\begingroup$ @DoHoaiPhuong: I can't do much until I get home tonight. By then, someone will most likely have helped you already. Cheers. $\endgroup$ – Kim Jong Un Oct 22 '14 at 15:33
  • $\begingroup$ Already 18 hours. Kim Jong Un,Have you solved this problem yet? you solved this problem yet? $\endgroup$ – Do Hoai Phuong Oct 23 '14 at 10:08
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    $\begingroup$ @DoHoaiPhuong: Your impatient demands are rude, and unlikely to spur interest in solving your problem. $\endgroup$ – copper.hat Oct 23 '14 at 14:48
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This problem can be solve using the knowledge about Harmonic conjugate and polar. Notice me if you need those information. enter image description here

hope this still can help.

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Thanks you for your solution. #Samara My solution: enter image description here

enter image description here

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