In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB= 75°.

Solution:

∠PAO = ∠ PBO = 90° ( angle b/w radius and tangent)

∠AOB = 105° (By angle sum property of a triangle)

∠AQB = ½ x105° = 52.5° (Angle at the remaining part of the circle is half the angle subtended by the arc at the centre)