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

Draw a circle through c.  Let's suppose the chords are parallel to the x and y axis, and that the points a and b lie on some large circle, and the lines $x=a$ and $y=b$ cross at $A, B$
We then have the equation that $A^2+B^2=C^2$ for the crossing, which gives these lines, and thence $A^2 + b^2 = a^2 + B^2 = R^2$,  which leads to the equation $a^2+b^2+c^2 = 2R^2$.
Answer:   $R^2 = (a^2+b^2+c^2)/2$
