In the given figure, BOC is a diameter of a circle with centre O
Question:

In the given figure, BOC is a diameter of a circle with centre O. If BCA = 30°, then ∠CDA = ?
(a) 30°
(b) 45°
(c) 60°
(d) 50°

 

Solution:

(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)

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