Question

in given figure if AT is a tangent to the circle with Centre O such that OT = 4 cm and angle OTA = 30°, then find the length of AT (in cm)​

Answer 1

Step-by-step explanation:

OT=4cm

/_T=30°

P/H=Sin30°

4/H=1/2 [sin30°=1/2]

H=8cm

hence proved

Answer 2

$\bf\huge\underline{Question}$

In given figure if AT is a tangent to the circle with Centre O such that OT = 4 cm and angle OTA = 30°, then find the length of AT (in cm)

$\bf\huge\underline{Answer}$

Join OA.

We know that, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, angle OAT = 90°

In ∆OAT, cos30° = $\dfrac{AT}{OT}$

=> $\dfrac{root3}{2}$ = $\dfrac{AT}{4}$

=> AT = 2√3 cm