Question 5
Trapezoid $ABCD$, with $\overline{AB} \parallel \overline{CD}$,
is inscribed in circle $\omega$ and point $G$ lies inside triangle $BCD$.
Rays $AG$ and $BG$ meet $\omega$ again at points $P$ and $Q$, respectively.
Let the line through $G$ parallel to $\overline{AB}$ intersect
$\overline{BD}$ and $\overline{BC}$ at points $R$ and $S$, respectively.
Prove that quadrilateral $PQRS$ is cyclic
if and only if $\overline{BG}$ bisects $\angle CBD$.
Proposed by Zuming Feng (credit in the supplied third-party notes).
is inscribed in circle $\omega$ and point $G$ lies inside triangle $BCD$.
Rays $AG$ and $BG$ meet $\omega$ again at points $P$ and $Q$, respectively.
Let the line through $G$ parallel to $\overline{AB}$ intersect
$\overline{BD}$ and $\overline{BC}$ at points $R$ and $S$, respectively.
Prove that quadrilateral $PQRS$ is cyclic
if and only if $\overline{BG}$ bisects $\angle CBD$.
Proposed by Zuming Feng (credit in the supplied third-party notes).