Triangle $ABC$ has an incircle $(I)$ which contacts $BC,CA,AB$ at $D,E,F$. On line $EF$ we get two points $M$ and $N$ such that $CM//BN//AD$. $DM$ and $DN$ cut $(I)$ at $P,Q$.
a, Prove that $BP,CQ,AD$ concur.
b, Let $J$ be point which $BP,CQ,AD$ concur. $X$ is midpoint of $PQ$. Show that $JX$ intersects $MN$ at the midpoint $G$ of $MN$.
I don't know which lemmas we use(maybe Ceva theorem, Thales theorem because there are three paralel lines). Show please and anyone can tell me some geometry book for studying? Thank.