In the figure above, 𝐴, 𝐵, and 𝐶 lie on the same line. 𝐵 is the center of the smaller circle, and 𝐶 is the center of the larger circle. If the diameter of the larger circle is 50, what is the radius of the smaller circle?

Solution: 12.5

The diameter of the larger circle is 50.

Therefore, radius of larger circle AC = 25 (as radius = diameter /2)

Now, AC is the diameter of the smaller circle

Therefore, radius of smaller circle = AC / 2 (diameter/2)

= 12.5.

Alternate solution:

From the figure given, it can be easily seen that,

Radius of smaller circle = 1/4 * (Diameter of bigger circle)

= 1/4 * (50)

= 12.5.