In the given figure, BOC is a diameter of a circle with centre O. If ∠BCA = 30°, then ∠CDA = ?

Question

In the given figure, BOC is a diameter of a circle with centre O. If ∠ BCA = 30°, then ∠ CD A = ?

Philoid · Accepted Answer

Given:

Here,

∠BAC = 90° (angle in the semicircle)

Now, in ΔABC

By angle sum property

∠BCA + ∠BAC + ∠ABC = 180°

30° + 90° + ∠ABC = 180°

∠ABC = 180° – 30° – 90°

∠ABC = 60°

Here,

∠ABC = ∠ADC (angles in the same segment)

∴ ∠CDA = 60°