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Angle Subtended by an Arc of a Circle on the Circle and at the Center

In the given ...

Question

In the given figure, if ∠ABC = 45°, then ∠AOC =

(a) 45°

(b) 60°

(c) 75°

(d) 90°

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Solution

(d) 90°

We have to find ∠AOC.

As we know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Hence, the correct answer is option (d).

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In the given figure, $∠ A O B = 90^{\circ} a n d ∠ A B C = 30^{\circ} . T h e n, ∠ C A O = ?$

(a) $30^{\circ}$

(b) $45^{\circ}$

(d) $90^{\circ}$

∠ A B C = 45^{\circ},

∠ A O C

∠ A O C = 60^{\circ}

∠ C A O

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