Question

If two tangents inclined at an angle of 60° are drawn to a circle of radius 4 cm, then the length of each tangent is equal to:

(a) 2√3 cm

(b) 8 cm

(c) 4 cm

(d) 4√3 cm

Answer 1

Correct option is (d) 4√3 cm

Consider a circle of radius 4 cm and center O. Tangents are drawn from point P to the circle at A and B.

A line form the center bisects the angle between the tangents. 

Hence, ∠APO = 30^∘

Also, ∠OAP = 90^∘ ....(Angle between tangent and the radius)

Thus, tan ∠APO = \(\frac{OA}{AP}\)

⇒ tan30^∘ = \(\frac{4}{AP}\)

⇒ AP = 4√3​ cm