Question

$O$ is centre of the circle. Find the length of radius, if the chord of length $24cm$ is at a distance of $9cm$ from the centre of the circle.

Answer 1

$OA$ is radius

$O$ is the centre of circle.

$AB$ is the chord and $OC\perp AB$

Segment between the centre of circle bisect the chord into two parts

$\therefore AC=CB=\frac{1}{2}AB$

$\therefore AC=CB=12$

Now $\Delta OCB$ is right angle triangle

$\therefore$ by Pythagoras theorem

$(OC{)}^2+(AC{)}^2=(OA{)}^2$

$(9{)}^2+(12{)}^2=(OA{)}^2$

$81+144=(OA{)}^2$

$225=(OA{)}^2$

$\therefore$ Taking square root both sides

$\therefore 15=OA$

$\therefore$ The radius of circle $15cm$