Inside a triangle $\Delta ABC$ We choose a point $P$. Then draw $BP$ and $CP$ to intersect $AC$ and $AB$ at $E$ and $F$ respectively . Then draw $EF$ to intersect the circumcircle of $\Delta ABC$ at $X$ and $Y$.
Then call the circumcenter of $\Delta PXY$ , $O'$.
Prove $O'P$ is perpendicular to $BC$ if and only if $\angle BAP= \angle CAP$
Made by myself
I guess I have seen $s^{th}$ similar in some European country TST in year $2014-2015$.
But we used it in an exam three day ago and no one solved and we got that our solution had a typo so we now want to find the correct answer.