Relation between chords length and radius of circle Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the circle),then find out the radius of the circle in terms of $a,b$ and $c$.Show some short-cut to do it quickly

Let $a'$, $b'$ be the lengths of the perpendiculars from $M$ to the chord of length $2a$, resp. $2b$. Then
$$c^2=a'^2+b'^2=(r^2-a^2)+(r^2-b^2)\ ,$$
from which we obtain
$$r=\sqrt{a^2+b^2+c^2\over2}\ .$$
