Question

Radius of the given circle is $2cm.$ Find the ratio of the angle $\angle D$ and $\angle A.$

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. None of the above.

Answer 1

The correct option is A $1:1$

We know that the angle subtended by an arc at the centre of a cirlce is double the angle subtended at any point on the circle.

Considering the arc CB and point D, $\angle O=2\times \angle D.$
$\Rightarrow \angle D=\frac{\angle O}{2}$
Considering the arc CB and point A, $\angle O=2\times \angle A.$
$\Rightarrow \angle A=\frac{\angle O}{2}$
$\therefore \angle D=\angle A$
$\Rightarrow \angle D:\angle A=1:1$