Question

p and PB are tangents drawn from a point P to the circle with Centre O if angle APB equal to 60 then what is angle aob

Answer 1

We know that tangent is always perpendicular to the radius at the point of contact.

So, ∠OAP = 90

We know that if 2 tangents are drawn from an external point, then they are equally inclined to the line segment joining the centre to that point.

So, ∠OPA = 12∠APB = 12×60° = 30°

According to the angle sum property of triangle-

In ∆AOP,∠AOP + ∠OAP + ∠OPA = 180°⇒∠AOP + 90° + 30° = 180°⇒∠AOP = 60°

 

So, in triangle AOP



Hence proved.