Question

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

Answer 1

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

To find the length of PQ, apply Pythagoras theorem in $△$OPQ since $\angle OQP={90}^{\circ }$

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

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

${QP}^2=625–49=576$

$QP=24cm$
The length of the tangent is 24 cm.