Question

In the given figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ____________.

Answer 1

Given:
AOB is a diameter of the circle
AC = BC


We know, the diameter subtends a right angle to any point on the circle.
∴ ∠ACB = 90° ...(1)

In ∆ACB,
AC = BC (given)
∴ ∠CAB = ∠CBA (angles opposite to equal sides are equal) ...(2)

Now,
∠CAB + ∠CBA + ∠ACB = 180° (angle sum property)
⇒ 2∠CAB + 90° = 180° (From (1) and (2))
⇒ 2∠CAB = 180° − 90°
⇒ 2∠CAB = 90°
⇒ ∠CAB = 45°

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Hence, ∠CAB is equal to 45°.