Question

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Answer 1

Question :-

AB is a diameter of a circle with centre O. C is a point on the circumference of the circle such that, ∠ CAB = 2 ∠ CBA. Find ∠ CBA.

Answer :-

Let ∠ CBA be x

So, ∠ CAB = 2x

We know that,

Angle in the semicircle is 90°.

So, ∠BCA = 90°

Applying angle sum property in ∆ ABC -

⇒ ∠CBA + ∠CAB + ∠BCA = 180°

⇒ x + 2x + 90 = 180

⇒ 3x + 90 = 180

⇒ 3x = 180 - 90

⇒ 3x = 90

⇒ x = 90 / 3

⇒ x = 30

Hence, ∠ CBA = 30°