Question

5. O is the centre of a circle with radius 9 cm. AT is
a tangent to the circle at the point T. II OA=41
cm, what is the length of AT"​

Answer 1

Answer:

OT = radius = 9 cm. AT tangent to the circle, OA = 41 cm. Tangents of a circle are perpendicular to the radius at the point of contact.

So, AT perpendicular to TO.

Consider triangle AOT.

Here, angle ATO = 90°

So, by Pythadoras Theorem, we have

OA² = OT² + AT²

=> 41² = 9² + AT²

=> 1681 = 81 + AT²

=> AT² = 1600

=> AT = 40

Hence, Length of AT = 40 cm