Question 5
Let $CD$ be a chord of circle $\Gamma_1$ and $AB$ a diameter of $\Gamma_1$ perpendicular to $CD$ at $N$, with $AN\gt NB$. A circle $\Gamma_2$ centred at $C$ with radius $CN$ intersects $\Gamma_1$ at $P,Q$, and segments $PQ,CD$ intersect at $M$. The radii of $\Gamma_1,\Gamma_2$ are $61,60$, respectively. Find $AM$.