Two tangents making an angle of 120 degree with each other are drawn to a circle of radius 6 cm then the length of each tangent is equal to .......?
Let P be the external points and PA and PB be the two tangents drawn to the circle with centre O.
Given : ∠APB = 120°
Also radius = OA = OB = 6 cm
We know that tangents drawn from an external point are equally inclined to the line joining that point to the centre
Now In ∆OAP
∠OAP = 90° (∵ Tangent is perpendicular to the radius at the point of contact)
Now in right ∆OAP
∠OPA = 60°
Also tangents drawn from an external point are equal in length
Hence the length of each tangent is cm.