# PQRS is a cyclic quadrilateral. If SQ bisect <PQR prove chord PS = chord SR

$PQRS$ is a cyclic quadrilateral. If $\overline{SQ}$ bisects $\angle PQR$ prove chord $\overline{PS}$ = chord $\overline{SR}$.

-
Sheesh, I already embedded the image for you and cleaned up your notation... – J. M. Aug 4 '11 at 13:11
thanks, I'm inexperienced with the notation on web and as a new user I couldn't embed an image. – MrK Aug 4 '11 at 13:13
Here's a sketch: $\angle PQS$ and $\angle RQS$ would be congruent, and thus subtend congruent arcs. Since $\stackrel{\frown}{PS}$ and $\stackrel{\frown}{SR}$ are congruent, then... – J. M. Aug 4 '11 at 13:16

Note that The Inscribed Angle Theorem says that $\angle PQS$ is half the central angle of chord $\overline{PS}$ and $\angle SQR$ is half the central angle of chord $\overline{SR}$. Since $\overline{SQ}$ bisects $\angle PQR$, $\angle PQS = \angle SQR$. Therefore, $\overline{PS}=\overline{SR}$ by SAS (side-angle-side).