Question

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle$ OTA = ${30}^o$ . Then AT = ?

(a) 4 cm (b) 2 cm

(c) $2\sqrt{3}$ cm (d) $4\sqrt{3}$ cm

Answer 1

Given;

OT = 4cm

$\angle$OTA= 30

consider the right triangle $△$OAT, right angled at A

$cos30=\frac{AT}{OT}\frac{\sqrt{3}}{2}=\frac{AT}{4}AT=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}$