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.