Intermediate Problems (2)

Two perpendicular chords of a circle $A_{1}A_{4}$ and $A_{2}A_{3}$ intersect at a point $P$ . If for $i=1, 2, 3, 4$ , the length of $PA_{i}=i$ , the radius of the circle can be expressed as $\frac{\sqrt{a}}{b}$ where $a, b$ are positive integers with $a$ square-free. Find $ab$ .

This problem is part of the set Intermediate Problems