Question

Find the length of the tangent of circle from an external point Q of distance $25$ cm. from center of circle O of redius $7$ cm?

Answer 1

We are given

length from external point $Q$ to $O=25cm$

radius $=7cm$

Let us take a point of $P$ and join $OP$. Since $OP$ is the radius of a circle with center $O$.

$△OPQ$ is a right angle triangle with $OP$ a perpendicular

So, using Pythagoras theorem

${OQ}^2={OP}^2+{PQ}^2$

$\Rightarrow$ ${25}^2={OP}^2+x^2$ (Let $PQ=x$ units)

$\Rightarrow$ $625=49+x^2$

$\Rightarrow$ $x=\sqrt{576}=24cm$