Question

The length of the tangent to a circle from a point $17cm$ from its centre is $8cm$. Find the radius of the circle.

Answer 1

Let $r$ be the radius of circle.

Given:-

$PQ=8cm$

$PO=17cm$

$OQ=r$

Since the tangent of any point of a line is perpendicular to the radius through the point of contact.

In $△OPQ$,

${OP}^2={PQ}^2+{OQ}^2\left(\text{By pythagoras theorem}\right)$

${\left(17\right)}^2={\left(8\right)}^2+r^2$

$\Rightarrow r=\sqrt{289-64}=\sqrt{225}=15cm$

Hence the radius of the circle is $15cm$.