Question 8
In the diagram, $ABCD$ is a quadrilateral where $\angle ABC=90^\circ$, $AB=9$, $BC=12$, $CD=39$ and $DA=36$. Circle $M$ is tangent to each side of $\triangle ABC$, and circle $N$ is tangent to each side of $\triangle ACD$. What is the ratio of the radius of circle $N$ to the radius of circle $M$?
