Question

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

 

Options

• 4 cm

• 2 cm

• `2sqrt3` cm

• `4sqrt3` cm

Answer 1

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to `underlinebb(2sqrt(3)  cm)`.

Explanation:

∠OAT = 30°     ...[∵ Tangent and radius are ⊥ to each other at the point of contact]

In right-angled ΔOAT,

`"AT"/"OT"` = cos 30°

⇒ `sqrt3/2="AT"/4`

⇒ `"AT" = (sqrt3xx4)/2`

⇒ AT = `2sqrt3` cm.