SEAMO 2027 - Paper F - SET 04 - Self-study Question 16

Let $CD$ be a chord of circle $T_1$, and let $AB$ be a diameter of $T_1$ perpendicular to $CD$ at $N$, with $AN>NB$. Circle $T_2$, centred at $C$ with radius $CN$, intersects $T_1$ at $P$ and $Q$, and segments $PQ$ and $CD$ intersect at $M$. Given that the radii of $T_1$ and $T_2$ are 61 and 60, respectively, find $AM$.