# Four on a circle

Author: mathforces
Problem has been solved: 43 times

Русский язык | English Language

The different points $P$, $Q$, $R$, $S$ lie on the circle $x ^ 2 + y ^ 2 = 25$ and have integer coordinates. The distances $PQ$ and $RS$ turned out to be irrational numbers. The largest possible value of the relation $\frac {PQ} {RS}$ is representable in the form $\frac{\sqrt {a}} {b}$, where $a$ and $b$ are coprime natural numbers. What is $a \cdot b$ equal to?