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Question
In the given figure, O is the centre of the circle. ∠OAB and ∠OCB are 30° and 40° respectively. Find ∠AOC . Show your steps of working.
Solution
Join AC,
Let ∠OAC = ∠OCA = x ...(Say)
∴ ∠AOC =180° – 2x
Also, ∠BAC = 30° + x
∠BCA = 40° + x
In ΔABC,
∠ABC =180° – ∠BAC – ∠BCA
= 180° – (30° + x) – (40°+ x)
= 110° – 2x
Now, ∠AOC = ∠2ABC
(Angle at the centre is double the angle at the circumference subtended by the same chord)
`=>` 180° – 2x = 2(110° – 2x)
`=>` 2x = 40°
∴ x = 20°
∴ ∠AOC = 180° – 2 × 20° = 140°
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