Question

From point $Q$, the length of the tangent to a circle is $15cm$ and the distance of $Q$ from the centre of circle is $17cm$, then find the radius of the circle

Answer 1

Let the centre of circle be $O$ and the tangent touches the circle at point $P$

Now $OP=r$ and triangle $OQP$ is right angles triangle

${OQ}^2={OP}^2+{PQ}^2{\left(17\right)}^2=r^2+{\left(15\right)}^2\Rightarrow r^2=289-225=64\Rightarrow r=\sqrt{64}=8$