Question

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then, AT = ?

Options

• 4 cm

• 2 cm

• `2sqrt(3)` cm

• `4sqrt(3)` cm

Answer 1

`bb(2sqrt(3)  cm)`

Explanation:

In right ΔOAT having right angle at A, we have

`cos(∠OTA) = (AT)/(OT)`

⇒ `cos 30^circ = (AT)/4`

⇒ `AT = (sqrt(3)/2 xx 4) cm`

⇒ `AT = 2sqrt(3)  cm`