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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
Solution
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.
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