In Fig, TA is a tangent to the circle with centre O such that OT = 4 cm, ?OTA = 30°, then length of TA is:

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Solution

Q.
In Fig, TA is a tangent to the circle with centre O such that OT = 4 cm, ∠OTA = 30°, then length of TA is:

1 $2 \sqrt{3} c m$

2 2 cm

3 $2 \sqrt{2} c m$

4 $\sqrt{3} c m$

Ans.
(1)

Since TA is tangent at A and OA is radius of the circle,
∴ $O A ⟂ T A \Rightarrow ∠ O A T = 90 °$

$∴ I n r i g h t a n g l e d Δ O A T, w e h a v e c o s 30 ° = \frac{T A}{O T} = \frac{\sqrt{3}}{2} \frac{T A}{4} = \frac{\sqrt{3}}{2} \Rightarrow T A = 2 \sqrt{3} cm$

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