Angle ate the area

Geometry Level 3

There are two circles. One with centre A [say circle A] whose radius is fixed and cannot be changed 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.

Right now point A, B and C are collinear as shown(assume 180°)

Now the point B is moved along the circumference of Circle A in anticlockwise direction such that angle \(CAB=90^\circ\) (assume) as shown in figure.

What is the ratio of the area of Circle C before movement of point B to area of Circle C after the movement of the point B

NOTE: 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.

These figures are just to give an idea about the question, so the assumptions can be taken as answers will be with respect to the assumptions.


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