Question

point M lies in the exterior of a circle with Centre A and a tangen from M touches the circle at an if AM=
41 cm and MN = 40 cm find the radius of the circle​

Answer 1

Radius of the circle is 9 cm.

Step-by-step explanation:

• This question can be solved using Pythagoras theorem.

• From the figure (refer the attached figure);

• We know that the radius is always perpendicular to the tangent.

• So, AN is perpendicular to MN.

• Now, the triangle $\Delta ANM$ is right angle, so Pythagoras theorem can be applied.

Therefore,

• $AM^2 = AN^2 + MN^2$

      $41^2 = radius^2 + 40^2$

       radius = AN

        1681 = $radius^2$ + 1600

      $radius^2$ = 1681 - 1600

        radius = $\sqrt{81} = \pm9$

Since, radius is the length. So, it must be positive.

Hence; radius = 9 cm