Question

In the figure 1, AT is the tangent to the circle with centre O such that $OT=4$ cm and $\angle OTA={30}^{\circ }$. Then the value of AT is equal to :

• A. 4cm
• B. 2cm
• C. $2\sqrt{3}$
• D. 8cm

Answer 1

Answer: (C)

$2\sqrt{3}$

AT is tangent to the circle

draw a line from O to A

OA will be the radius of a circle

because AT is tangent to the circle

$\angle OAT=90$ and hypotenuse $OT=4cm$

now apply $\cos 30$=$\frac{base}{hypotenuse}$

$\cos 30=\frac{\sqrt{3}}{2}=\frac{AT}{4}$

There $AT=2\sqrt{3}$

so option c will be the answer.