In Fig. 16.120, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.
Answers
Given : O is the centre of the circle and ∠APB = 50°.
We have , ∠APB = 50°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∠AOB = 2∠APB
∠AOB = 2 × 50
∠AOB = 100°
Since,
OA = OB (Radius of the circle)
∠OAB = ∠OBA (Angle opposite to equal sides are equal)
Let, ∠OAB = ∠OBA = x
In ∆ OAB,
We know that , sum of all the angles of a triangle is 180°.
∠OAB + ∠OBA + ∠AOB = 180°
x + x + 100° = 180°
2x + 100° = 180°
2x = 180° 100°
2x = 80°
x = 80°/2
x = 40°
∠OAB = ∠OBA = 40°
Hence, ∠AOB is 100° and ∠OAB is 40°.
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