#### Write ‘True’ or ‘False’ and justify your answer in each of the following : If a chord AB subtends an angle of $60^{\circ}$ at the centre of a circle, then angle between the tangents at A and B is also $60^{\circ}$.

Solution

Here CA and CB are the two tangents which is drawn on chord AB and also we know that tangent and radius are perpendicular to each other.
i.e., $\angle CBO=\angle CAO= 90^{\circ}$
$\angle A+\angle B+\angle C+\angle O= 360^{\circ}$
[$\mathbb{Q}$  Sum of interior angles of a quadrilateral is $360^{\circ}$]
$90^{\circ}+90^{\circ}+\angle C+60^{\circ}= 360^{\circ}$
$\angle C= 360^{\circ}-60^{\circ}-90^{\circ}-90^{\circ}$
$\angle C= 120^{\circ}$

Here we conclude that angle between the tangents at A and B is $120^{\circ}$.

Therefore the given statement is False.