Question

lfs the angle between two tangent drawn from an external point P to a circle of a radius a and centre o, is 60 degree , then find the length of op

Answer 1

Radius = a

Let the tangents be AP and BP

Then angle APB = 60 degrees

Construction: Join OP

Now, in triangle OPA

Angle PAO = 90 degrees

Angle POA = 180 - (90 + 30)

= 60 degrees

Now, in triangle

cos O = B/H

cos O = OA/OP

cos 30 = a/H

√3/2 = a/H

√3H = 2a

OP = (2a/√3) u