Question

If ∠𝑂𝐴𝐵 = 40° and 𝐴𝐵 = 𝐶𝐷, then find the measure of ∠𝐶𝑂𝐷.

Answer 1

Construction: Draw lines OB, OC, and OD.
In ΔAOB,
OA = OB (Radii of the same circle)
Thus, ∠OAB = ∠OBA = 40°.
(Angles opposite to equal sides of a triangle).
So, by angle sum property, ∠AOB = 100°.

Since the chords AB and CD are equal in length, the angles subtended by them at the centre will be equal.

Hence, ∠AOB = ∠COD = 100°.