In the given figure, O is the centre of the circle.

Question:

In the given figure, O is the centre of the circle. If ACB = 50°, find ∠OAB.

 

Solution:

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference.
AOB = 2ACB

 = 2 × 50°      [Given]

AOB = 100°       ...(i)
Let us consider the triangle ΔOAB.
OA = OB (Radii of a circle)
Thus, OAB = OBA 
In ΔOAB, we have:
AOB + OAB OBA = 180°
⇒ 100° + OAB + OAB = 180°
⇒ 100° + 2OAB = 180°
⇒ 2OAB = 180° – 100° = 80°
⇒ OAB = 40°
Hence, OAB = 40°

 

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