Question 23
Let $AM$ and $AN$ be the tangent lines to a circle $\Gamma$ drawn from a point $A$ ($M$ and $N$ belong to the circle). A line through $A$ cuts $\Gamma$ at $B$ and $C$ with $B$ between $A$ and $C$, and $\frac{AB}{BC} = \frac{2}{3}$.
If $P$ is the intersection point of $AB$ and $MN$, calculate $\frac{AP}{PC}$.
If $P$ is the intersection point of $AB$ and $MN$, calculate $\frac{AP}{PC}$.