Question

If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.

Answer 1

The given diagram illustrates the situation explained in the problem.

According to the question,we need to find the length PO.

We know that in a circle, the radius (OA) is always perpendicular to the tangent (PA).

Hence, $\angle PAO={90}^{\circ }$.

Applying Pythagoras theorem,
we get,

$P{O}^2=P{A}^2+O{A}^2$

$\Rightarrow P{O}^2={12}^2+5^2=169$
$\Rightarrow PO=13cm$.