Question

In the given figure, BOC is a diameter of a circle with centre O. If $\angle BCA={30}^{\circ }\text{then}\angle CDA=?$

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${50}^{\circ }$

Answer 1

(c) 60°

Angles in a semi circle measure 90°.
∴ ∠BAC = 90°
In Δ ABC, we have:
∠BAC + ∠ABC + ∠BCA = 180° (Angle sum property of a triangle)
∴ 90° + ∠ABC + 30° = 180°
⇒ ∠ABC = (180° - 120°) = 60°
∴ ∠CDA = ∠ABC = 60° (Angles in the same segment of a circle)