9 In the figure below the smaller circle touches the larger

9. In the figure below, the smaller circle touches the larger circle internally. Rectangular axes pass through the centre of the larger circle. Find the diameters of the two circles. adapted from Bertollo, Bob Touching Circles. Mathematical Spectrum 46(1):29 (2013) ] 24

Solution

We have given that the rectangular axes passes through the center of larger circle.

Also we have given the distance from one point on larger circle to one point on smaller circle as 9.

You can see that the distance from point on smaller circle to the center of larger circle is same as distance from point on larger circle to the point on smaller circle.

Hence distance from point on smaller circle to the center of axes = 9

Hence the distance from point on larger circle to the center of axes = 9 + 9 = 18

You will get this distance as the radius of the bigger circle.

Use the concept that diameter = 2 * radius and find the diameter of the larger circle.

The internal circle tangent to the external and containing the center of external circle, has as diameter the radius of the external.

Use the concept that diameter of internal circle = radius of external circle and find the diameter of the smaller circle.

Hope this will help .

Thank you.