In Fig.10.5, if AOB is a diameter of the circle and AC = BC, then CAB is equal to:

Question

Philoid · Accepted Answer

Given: AOB is the diameter of the circle.

AC = BC

⇒ ∠ABC = ∠BAC = x (say) (∵ angles opposite to equal sides are equal)

Also, diameter subtends a right angle to the circle,

∴ ∠ACB = 90°

Now, by angle sum property of a triangle, sum of all angles of a triangle is 180°.

∴ ∠CAB + ∠ABC + ∠ACB = 180°

⇒ x + x + 90° = 180°

⇒ 2x = 90°

⇒ x = 45°

∴ ∠CAB = ∠ ABC = 45°