Circle the circle

Geometry Level 3

There are two circles. One with centre A [say circle A] of radius 10 cm and one with center C [say circle C] whose radius can be varied with the help of a point B which lies on the circumference of the circle with center A.

The point B is bound to move only on the circumference of the circle A. And the point C stays at one point and cannot move.

What will be the minimum diameter of the circle C so that the circle A is completely inside the circle C?

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