Question

Find the length of the tangent drawn from a point P to a circle with centre O and radius 7 cm. Given OP = 25 cm.

Answer 1

Using pythagoras theorem,

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

$\Rightarrow {OQ}^2+{24}^2={25}^2$

$\Rightarrow {OQ}^2={25}^2-{24}^2$

$\Rightarrow {OQ}^2=625-576=49$

$\Rightarrow OQ=\sqrt{49}=7$cm

$\therefore$ Radius of the circle is $7$cm