Question

In the figure given below, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $AB=24cm,OM=5cm,ON=12cm$. Find the
Radius of the circle

Answer 1

Given: $AB=24cm;OM=5cm,ON=12cm$.
$\because OM\perp AB$
$M$ is mid point of $AB$.
$\therefore AM=12cm$.
Let radius of circle $=r$
From $△AMO;A{O}^2=A{M}^2+O{M}^2$ (By Pythagoras theorem)
$r^2=(12{)}^2+(5{)}^2$
$=144+25=169$
$r=13cm$.