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प्रश्न
In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108°, find: ∠ADB.
उत्तर
Again, Arc AB subtends ∠AOB at the centre and
∠ACB at the remaining part of the circle.
∠ ACB = `1/2` ∠AOB
=` 1/2 xx 108°`
= 54
In cyclic quadrilateral ADBC
∠ADB + ∠ACB = 180° ...[sum of opposite angles]
⇒ ∠ADB + 54° = 180°
⇒ ∠ADB = 180° − 54°
⇒ ∠ADB = 126°
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