In the given figure, O is the centre of the circle, and ∠OAB=20° and ∠OCB=50°. Find ∠AOC.
A
60°
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B
70°
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C
50°
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D
20°
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Solution
The correct option is A 60° OA=OC (radii of the same circle) ∠OAB=∠OBA=20°
In OAB, ∠OAB+∠AOB+∠BOA=180° 20°+20°+∠BOA=180° ∠BOA=140° OB=OC (radii of the same circle) ∠OBC=∠OCB=50°
In OCB, ∠OBC+∠OCB+∠COB=180° 50°+50°+∠COB=180° ∠COB=80° ∠AOB=∠AOC+∠BOC ∠AOC=∠AOB−∠BOC ∠AOC=140°−80° ∠AOC=60°