Question 97
Let $ABC$ be a triangle such that $A = 105^\circ$ and $B = 45^\circ$. Let $L$ be a point in $BC$ such that $AL$ is the bisector of $BAC$ and $M$ be the midpoint of $AC$. If $AL$ and $BM$ meet at the point $P$, calculate the ratio $\frac{AP}{AL}$.