Consider the above figure where O is the center of the circle, AB = CD and $∠ A O B = 30^{\circ} .$ Find $∠ A E D$ and $∠ C O D$ .

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Solution

Given that $A B = C D$
We know that equal chords subtend equal angles at the centre.
$⟹ ∠ A O B = ∠ C O D = 30^{\circ}$
$⟹ ∠ A E D = 90^{\circ}$
$∴ ∠ A E D = 90^{\circ}$ and $∠ C O D = 30^{\circ}$

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Similar questions

Consider the above figure where $O$ is the center of the circle, $A B = C D$ and $∠ A O B = 30^{\circ} .$ Then, $∠ A E D$ = ___ and $∠ C O D$ = ___.

A B = C D

∠ A O B = 90^{o}

∠ C O D

∠ A O B = 30^{\circ}

∠ C O D

A B = C D

∠ A O B = 90^{0}

∠ C O D .

A B

C D

∠ A O B = 50^{o}

∠ C O D = ?

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