Question

Consider the above figure where $O$ is the center of the circle, $AB=CD$ and $\angle AOB={30}^{\circ }.$ Then, $\angle AED$ = ___ and $\angle COD$ = ___.

• A. ${60}^{\circ },{30}^{\circ }$
• B. ${30}^{\circ },{90}^{\circ }$
• C. ${90}^{\circ },{30}^{\circ }$
• D. ${80}^{\circ },{50}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ },{30}^{\circ }$

Given that $AB=CD.$ We know that equal chords subtend equal angles at the centre.
$⟹\angle AOB=\angle COD={30}^{\circ }$
Also, we know that angle at the circumference in a semicircle is a right angle.
$⟹\angle AED={90}^{\circ }$
$\therefore \angle AED={90}^{\circ }$and $\angle COD={30}^{\circ }$