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Question
In following figure , O is the centre of the circle. If ∠ APB = 50° then find ∠ AOB and ∠ OAB.
Solution
Since arc AB makes ∠ AOB at the centre and ∠ APB = 500 on the remaining part of the circle.
∠ AOB = 2 ∠ APB
∠ AOB = 2(50) = 100°
AO= OB = x (radii of same circle)
In Δ AOB
∠ AOB + ∠ BAO + ∠ ABO = 180
180 + x + x = 180
2x = 80
x = 40
∴ ∠ OAB = 40°
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