Question 66
Two circles $k_{1}$ and $k_{2}$ intersect at points $A$ and $B$. A circle $k_{3}$ centered at $A$ meets $k_{1}$ at $M$ and $P$ and $k_{2}$ at $N$ and $Q$, such that $N$ and $Q$ are on different sides of $MP$ and $AB \gt AM$.
Prove that the angles $\angle MBQ$ and $\angle NBP$ are equal.
Prove that the angles $\angle MBQ$ and $\angle NBP$ are equal.