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Q.

What will be the value of ∠BOC, if in the given figure, O is the centre of a circle in which ∠OBA = 20° and ∠OCA = 30°?

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a

50 ∘

b

90 ∘

c

100 ∘

d

130 ∘

answer is C.

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Detailed Solution

It is given that O is the centre of a circle in which ∠OBA = 20° and ∠OCA = 30°.
We have to find the value of ∠BOC.
Question Image

Question Image

It is clear from the figure that OA, OB, and OC are the radius of the circle, so they are equal.
We know that in an isosceles triangle, the angles, which are opposite to the equal sides of an isosceles triangle, are always equal.
Also, triangle OAB and OAC are isosceles triangles, having equal sides OA, OB and OA, OC respectively.
Therefore,

∠ O A B = ∠ O B A

and

∠ O A C = ∠ O C A

So,

∠ B A C = ∠ O A B + ∠ O A C ⇒ ∠ B A C = 200 + 300 (∠ O A B = 200 & ∠ O A C = 300) ⇒ ∠ B A C = 500

Now,

∠ B A C = 12 (∠ B O C) ⇒ ∠ B O C = 2 (∠ B A C) = 1000

So, the value of

∠ B O C = 1000

.
Therefore, option 3 is correct.

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