Question

In a circle, O is the centre and AB is a chord of length 24 cm. The distance of AB from O is 10 cm then find the radius of the circle.

Answer 1

Length of chord AB $=24cm$

The distance of chord AB from centre $=10cm$

We know that line joining the centre of the circle to the chord is perpendicular to the chord.

Therefore, in the above figure $OC\perp AB$

Applying Pythagoras theorem in triangle AOC we get,

$A{O}^2=O{C}^2+A{C}^2$, where

$AC=\frac{24}{2}=12cm$ and $OC=10cm$

Then,

$A{O}^2={12}^2+{10}^2$

$A{O}^2=144+100$

$AO=\sqrt{155}cm$