Question

23. Point M lies in the exterior of
a circle with centre a and a tangent from
M touches the circle at n
if AM 41 cm and MN = 40 cm, find the
radius of the circle.​

Answer 1

Answer:

The radius of the circle is 9 cm.

Step-by-step explanation:

M lies in the exterior of a circle with Centre A

AM = 41cm

Tangent from M touches the circle at point N on the circle.

MN = 40cm

Join Centre A and Point N

AN becomes the radius.

Since, tangent drawn to the circle is perpendicular to the radius of the circle, we get,

MN is perpendicular to AN

Angle ANM or Angle N = 90°

∆ ANM is a right angled triangle.

Side opposite to 90° angle is the hypotenuse.

Therefore, AM is the hypotenuse of the ∆ ANM

Using Pythagorean Theorem,

AM² = MN² + AN²

(41)² = (40)² + AN²

1681 = 1600 + AN²

AN² = 1681 - 1600

AN² = 81

Taking square roots on both the sides, we get,

AN = √(81)

AN = 9 cm