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4. In the fig. O is the centre of the circle. find angle AOB |
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Answer» 100°Step-by-step EXPLANATION:Join OCOA= OC (Radii of Circle)∠OAC=∠OCA= 20° (Angle OPPOSITE to EQUAL sides are equal to each other)Similarly, OC=OB (Radii of Circle)∠OBC=∠OCB= 30° (Angle opposite to equal sides are equal to each other)∠ACB=∠OCA+∠OCB∠ACB= 20°+30°∠ACB= 50°2∠ACB= ∠AOB (Theorem 10.8)2(50)= ∠AOB100°= ∠AOBNOTE:- Theorem 10.8 states that 'The angle subtended by the arc at the center is double the angle subtended by it at any POINT on the remaining part of the circle.'Hope It Helps :) |
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