ONM 2014 problema 4

[Doctor Gil]

In triunghiul $\triangle{ABC}$ consideram punctele $M,N\in (AB)$, $P, Q\in (BC)$ si $S,R \in (AC)$ astfel incat $AM=CR, AN=CS$, $\angle{MQB}\equiv \angle{RQC}$ si $\angle{NPB}\equiv \angle{SPC}$.
Aratati ca daca $MQ+QR=NP+PS$, atunci triunghiul $\triangle{ABC}$ este isoscel.