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.

hellothere Jul 15, 2021

#1**0 **

This is the same one that I looked at the other day.

I know I did not answer it, but I did go to the effort to draw a comprehensive pic. Which you completely ignored.

Anyway, it does not matter that I did anything at all.

This is a repost hence you need to guide people to the original question.

You need to include a hyperlink to the original and request that people answer on the original.

And for them to just leave a little note here saying that they have done so.

If you ever need an original question unlocked then send a polite note to a moderator asking them to open it for you.

Melody Jul 15, 2021