Question

Find the length of a tangent drawn from a point, which is $15cm$ away from centre of circle having $9cm$ as radius.

Answer 1

Since, $OQ=9cm$ and $OP=15cm$

To find: $PQ=?$

By Pythagoras theorem,

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

${\left(9cm\right)}^2+{PQ}^2={\left(15cm\right)}^2$

${PQ}^2=225c{m}^2-81{cm}^2$

${PQ}^2=144{cm}^2$

$PQ=\sqrt{144{cm}^2}$

$PQ=12cm$

Length of the tangent $=12cm$