IMO Shortlist 2005 G6
The median $AM$ of triangle $ABC$ intersects the incircle $\omega$ at $K$ and $L$. The lines through $K$ and $L$ parallel to $BC$ intersects $\omega$ again at $X$ and $Y$. The line $AX$ and $AY$ intersect $BC$ at $P$ and $Q$. Prove that, $BP=CQ$.
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Re: IMO Shortlist 2005 G6
Hint:
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: IMO Shortlist 2005 G6
Yeah, Zhao is always awesome. I proved that lemma (also the whole problem) using projective geometry. This solution is (almost) the same as mine. So no need to post again.