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Question

In the given figure, O is the centre of a circle in which OBA=20 and OCA=30. Then, BOC=?

(a) 50

(b) 90

(c) 100

(d) 130


Solution

ANSWER:
( c ) 100°
In Δ OAB, we have:
OA = OB
(Radii of a circle)
⇒ ∠OAB = ∠OBA = 20°
In ΔOAC, we have:
OA = OC
(Radii of a circle)
⇒ ∠OAC = ∠OCA = 30°
Now, ∠BAC = (20° + 30°) = 50°
∴ ∠BOC = (2 × ∠BAC) = (2 × 50 °) = 100°

Mathematics
Secondary School Mathematics IX
Standard IX

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