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In a cyclic quadrilateral ABCD, ∠BCD = 120° and passes through the centre of the circle. Then ∠ABD = ?
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- 30°
- 40°
- 50°
- 60°
- 30°
Correct Option: A
As per the given in question , we draw a figure of cyclic quadrilateral ABCD
As we know that the sum of opposite angles of a concyclic quadrilateral is 180°.
∴ ∠BCD + ∠BAD = 180°
⇒ 120° + ∠BAD = 180°
⇒ ∠BAD = 180° – 120° = 60°
The angle in a semi-circle is a right angle.
∴ ∠BDA = 90°
∴ In ∆ABD,
∴ ∠ABD = 90° – 60° = 30°
