Question 97
In triangle $ABC$, points $D,E\in(BC)$, $F,G\in(CA)$ and $H,I\in(AB)$ satisfy $BD=CE$, $CF=AG$ and $AH=BI$. Let $M,N,P$ be the midpoints of $GH,DI,EF$, respectively, and let $M'=AM\cap BC$.
a) Prove that $\displaystyle\frac{BM'}{CM'}=\frac{AG}{AH}\cdot\frac{AB}{AC}$.
b) Prove that $AM,BN,CP$ are concurrent.
a) Prove that $\displaystyle\frac{BM'}{CM'}=\frac{AG}{AH}\cdot\frac{AB}{AC}$.
b) Prove that $AM,BN,CP$ are concurrent.