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Problem: In triangle ABC with incenter I and circumcenter O. Let P be the reflection of A over OI and Q be the second intersection of line OI with the circumcircle of BIC. Prove that lines AI, BC, and PQ concur. 

 

So for this problem I got that from the incenter-excenter lemma, the center of the circumcircle of BIC must be the midpoint of arc BC or triangle ABC, also, I let AI intersect BC at E and it is not to show that P, E and Q and collinear, but I don't really know how to do that, can anyone give me hints or solutions? Thanks. Also I would prefer not advanced topics such as inversion, complex bash, or barcentrics, thanks. 

 Jul 4, 2021
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You can use inversion on the problem.

 Jul 4, 2021

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