[ The product of the lengths of the chord segments and the lengths of the secant segments ]

A point $M$ inside a circle divides a chord of this circle into segments equal to $a$ and $b$. Through point $M$, a chord $A B$ is drawn, which is bisected by point $M$. Find $A B$.
According to the theorem of intersecting chords, $A B^{2}=4 a b$.

## Answer

$2 \sqrt{a b}$.