Question 16
An engineer constructs a circle with centre $O$ and diameter $CD$ on level ground, and builds a vertical tower of height $20$ at the centre. $B$ is another point on the circumference and $P$ is on $CD$ produced such that $PB$ is a secant line of the circle. Given that $PB=33$, $PC=77$ and $CD=74$, find the minimum possible distance of any point on $PB$ to the top of the tower.
