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11. Circles
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Q12 of 141 Page 464

In the given figure, O is the centre of a circle and ∠ABC = 45°. Prove that OA ⊥ OC.

Given: ∠ABC = 45°


We know that ,


∠ AOC = 2×∠ABC


∠ AOC = 2×45 = 90°


∴ ∠AOC = 90°


Therefore


Hence proved.


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10

A circle with centre O is given in which ∠OBA = 30° and ∠OCA = 40°. Find ∠BOC.

11

In the given figure, AOC is a diameter of a circle with centre O and arc arc BYC. Find ∠BOC.

13

In the given figure, O is the centre of a circle, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

14

In the given figure, O is the centre of a circle, ∠ACB = 40°. Find ∠OAB.

Questions · 141
11. Circles
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