In figure, AT is a tangent to the circle with center 0 such that OT = 4 cm and ∠OTA = 30°. Then, AT is equal to

Question

In figure, AT is a tangent to the circle with center 0 such that OT = 4 cm and ∠ OTA = 30°. Then, AT is equal to

Philoid · Accepted Answer

Given : A circle with center O and a tangent AT passing through point A on the circle, also OT = 4 cm and ∠OTA = 30°

To find : Length of AT

Construction : Join OA.

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

So we have

OA ⏊ AT

Therefore, ∠OAT = 90°

In △ OAT

Using

We have,