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Question
In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; find:
- ∠ACB,
- ∠OBC,
- ∠OAB,
- ∠CBA.
Solution
Here, `∠ACB = 1/2 "Reflex" (∠AOB)`
= `1/2 (360^circ - 140^circ)`
= 110°
(Angle at the centre is double the angle at the circumference subtended by the same chord)
Now, OA = OB (Radii of same circle)
∴ ∠OBA = ∠OAB
= `(180^circ - 140^circ)/2`
= 20°
∴ ∠CAB = 50° – 20° = 30°
ΔCAB,
∠CBA = 180° – 110° – 30° = 40°
∴ ∠OBC = ∠CBA + ∠OBA
= 40° + 20°
= 60°
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