Question 45
Let $PA$ and $PB$ be the tangents to a circle $\omega$ from an external point $P$. Let $M$ and $N$ be the midpoints of $AP$ and $AB$, respectively. Extend $MN$ to meet $\omega$ at $C$, where $N$ is between $M$ and $C$. The line $PC$ meets $\omega$ again at $D$, and the extension of $ND$ meets $PB$ at $Q$. Show that $MNQP$ is a rhombus.