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 $\angle BOC$.


  • $\begingroup$ 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

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.


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

enter image description here


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