Question

In the given figure, ∠BOQ = 60° and AB is diameter of the circle. Find ∠ABO.

• A. 20°
• B. 30°
• C. 40°
• D. 50°

Answer 1

Answer:

B. 30°

Using the theorem, angle in the semi-circle is a right angle,

⇒ ∠BOA = 90°

Theorem: The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

⇒ ∠BOQ = ∠BAO = 60°

In ΔABO,

Sum of the angles of the triangle is 180°

⇒ ∠ABO = 180° – ∠BOA – ∠BAO = 180° – 90° – 60° = 30°