Mathematics
In the given figure, O is center of the circle. Chord BC = chord CD and angle A = 80°. Angle BOC is :
120°
80°
100°
160°
Circles
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Answer
Given,
Chord BC = chord CD
∴ ∠BOC = ∠COD = x (let)
From figure,
∠BOD = ∠BOC + ∠COD = x + x = 2x
We know that,
The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.
⇒ ∠BOD = 2∠BAD
⇒ 2x = 2 × 80°
⇒ x = 80°.
Hence, Option 2 is the correct option.
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