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°
​

Answer 1

Answer:

YOUR ANSWER IS 60°.

OPTION (C) IS CORRECT

Step-by-step explanation:

(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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