Question

two tangents make an angle of 120 degree with each other are drawn the circle of radius 6 CM show that the length of tangent is 2 √ 3 CM.​

Answer 1

Step-by-step explanation:

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.