Question

If tangents $RA$ and $RB$ from a point $R$ to a circle with centre $O$ are inclined to each other at an angle of $\theta$ and $\angle AOB={40}^o$ then find the value of $\theta$ (in degrees).

Answer 1

In the above figure, by using the property that the tangent and radius at the point of contact are perpendicular to each other. So,

$\angle A={90}^o$

$\angle B={90}^o$

Now, by using the angle sum property in quadrilateral $AOBR,$

$\angle AOB+\angle OAR+\angle OBR+\angle ARB={360}^o$

$\Rightarrow {40}^o+{90}^o+{90}^o+\theta ={360}^o$

$\Rightarrow \theta ={140}^o$