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Question

In the given figure, if ∠OAB = 40∘ , then ∠ACB = ____________


Solution

Given:
OAB = 40°      ...(1)


In ∆OAB,
OA = OB
∴ ∠OAB = OBA = 40° (angles opposite to equal sides are equal)    ...(2)

Now,
OAB + OBA + AOB = 180° (angle sum property)
⇒ 40° + 40°AOB 180°   (From (1) and (2))
⇒ ∠AOB = 180° −  80°
⇒ ∠AOB = 100°  ...(3)


We know, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
Thus, ∠AOB = 2∠ACB
⇒ 100° = 2∠ACB    (From (3))
⇒ ∠ACB = 50°


Hence, ∠ACB50°.

Mathematics
RD Sharma (2019)
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