A,B and C are the three points on a circle such that $$\angle$$ABC = $$35^{0}$$ and $$\angle$$BAC = $$85^{0}$$. What is the angle (in degrees) subtended by arc AB at the center of the circle? ?->(Show Answer!)

1. A,B and C are the three points on a circle such that $$\angle$$ABC = $$35^{0}$$ and $$\angle$$BAC = $$85^{0}$$. What is the angle (in degrees) subtended by arc AB at the center of the circle?

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By: anil on 05 May 2019 03.04 pm

Given : $$angle$$ABC = $$35^circ$$ and $$angle$$BAC = $$85^circ$$ To find : $$angle$$ AOB = ? Solution : In triangle, ABC => $$angle A+angle B+angle C=180^circ$$ => $$85^circ+35^circ+angle C=180^circ$$ => $$angle C=180^circ-120^circ=60^circ$$ Now, angle subtended by an arc at the centre is double the angle subtended by it at any point on the circle. => $$angle AOB=2 imesangle ACB$$ = $$2 imes60^circ=120^circ$$ => Ans - (D)

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