Question

A point $P$ is at a distance of $25cm$ from the centre of a circle. The radius of the circle is $7cm$ and length of the tangent drawn from $P$ to the circle is $xcm.$ The value of $x$ is ___ $cm.$

Answer 1

Given that $OP=25cm$ and $OQ=7cm.$

To find the length of PQ, apply Pythagoras theorem in $△$OPQ.

$\Rightarrow {OQ}^2+{QP}^2={OP}^2$

$\Rightarrow 7^2+{QP}^2={25}^2$

$\Rightarrow {QP}^2=625–49=576$

$\Rightarrow QP=24cm$
Thus, the length of the tangent is $24cm.$