Question

Construct a pair of tangents to a circle of radius $3cm$, which are inclined to each other at an angle of ${60}^{\circ }$

Answer 1

Given angle between tangents is ${60}^0$.

i.e $\angle QPR={60}^0$

Since Angle at center is double the angle between tangents

$\therefore \angle OQR=2\times {60}^0={120}^0$

Draw a circle with centre O and radius 3 cm.
$\therefore$ we draw a radius, then second radius at ${120}^0$ from first.

Also,Tangents is perpendicular to radius.

So, $OQ\perp QP\&OR\perp PR$

Thus, to make tangents,

we draw perpendicular from poilnt $Q$ and $R$

So, we draw ${90}^0$ from point $Q$ and point $R$