Question

If ∠𝑂𝐴𝐵 = 50° and 𝐴𝐵 = 𝐶𝐷, then find the measure of ∠𝐶𝑂𝐷.

Answer 1

Here, we are given chords AB and CD of equal length.
Construct lines connecting points B, C, and D with the centre of the circle ‘O’.
In △OAB,
OA = OB (Radii of a circle)
∠OAB = ∠OBA (The sides opposite to equal angles of a triangle are equal)
∠OAB = ∠OBA = 50°
∠OAB + ∠AOB + ∠OBA = 180° (Angle sum property of the triangle)
∠AOB = 180° − 50° − 50° = 80°
∴ ∠AOB = 80°
∠AOB = ∠COD (Angles subtended by equal chords at the centre of a circle)
∴ ∠COD = 80°
Answer: ∠COD = 80°