Question

A tangent from $P$, a point in the exterior of a circle touches circle at $Q$. If $OP=13$, $PQ=5$, then the diameter of the circle is ______________

• A. $576$
• B. $15$
• C. $8$
• D. $24$

Answer 1

The correct option is D $24$

Since tangent is perpendicular to the radius through the point of contact
so, $PQ\perp OQ$

therefore
${\left(PQ\right)}^2+{\left(OQ\right)}^2={\left(OP\right)}^2$

$={\left(5\right)}^2+r^2={\left(13\right)}^2$

$=r^2=169-25$

$\Rightarrow r^2=144$

$\Rightarrow r=12cm$

so, diameter of the circle $2\times r$
$=2\times 12$ $=24cm$