# Intermediate Problems (2)

Geometry Level pending

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

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