Question

In the given figure, PAQ is the tangent. BC is the diameter of the circle. ∠BAQ = 60°, find ∠ABC.

 

Options

• 25°

• 30°

• 45°

• 60°

Answer 1

30°

Explanation:

Join OA

As the tangent at any point of a circle is perpendicular to the radius through the point of contact.

∠OAQ = 90°

∠OAB = ∠OAQ - ∠BAQ

∠OAB = 90° - 60°

∠OAB = 30°

OA = OB (radius)

∠OAB = ∠OBA

Therefore ∠OBA = 30°

∠ABC = 30°