Question 69
In triangle $ABC$ points $M, N \in (AB)$, $P, Q \in (BC)$ and $S, R \in (AC)$ are taken such that $AM = CR$, $AN = CS$, $\overline{MQB} \equiv \overline{RQC}$ and $\overline{NPB} \equiv \overline{SPC}$.
Show that if $MQ + QR = NP + PS$, then triangle $ABC$ is isosceles.
Show that if $MQ + QR = NP + PS$, then triangle $ABC$ is isosceles.