In the given figure, AT is a tangent to the circle with center O such

1.	In the given figure, AT is a tangent to the circle with center O such that OT = 4 cm and ∠OTA = 30°, Then, AT = ?(a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm
Answer» Correct answer is (c) 2√3 cm OA ⊥ AT So, \(\frac{AT}{OT}=\) cos 30° \(\Rightarrow\) \(\frac{AT}{4}=\frac{\sqrt{3}}{2}\) \(\Rightarrow\) AT = \((\frac{\sqrt{3}}{2}\times4)\) \(\Rightarrow\) AT = \(2\sqrt{3}\)

In the given figure, AT is a tangent to the circle with center O such that OT = 4 cm and ∠OTA = 30°, Then, AT = ?(a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm

Answer»

Correct answer is (c) 2√3 cm

OA ⊥ AT

So, \(\frac{AT}{OT}=\) cos 30°

\(\Rightarrow\) \(\frac{AT}{4}=\frac{\sqrt{3}}{2}\)

\(\Rightarrow\) AT = \((\frac{\sqrt{3}}{2}\times4)\)

\(\Rightarrow\) AT = \(2\sqrt{3}\)

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In the given figure, AT is a tangent to the circle with center O such that OT = 4 cm and ∠OTA = 30°, Then, AT = ?(a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm

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