Question

Draw a circle of diameter $10cm$. From a point $P,13cm$. away from its centre, draw the two tangents $PA$ and $PB$ to the circle and measure their lengths.

Answer 1

Tangent and radius will be perpendicular so $\angle PAO={90}^o$

OA = radius of circle $=5cm$

Given $OP=13cm$

By pythagoras theorem ${PO}^2={OA}^2+{AP}^2$

So length of the tangents are

$PA=PB=\sqrt{{PO}^2-{OA}^2}=\sqrt{{13}^2-5^2}=\sqrt{169-25}=\sqrt{144}=12$

$PA=PB=12cm$