(c) is a circle of center O and radius R=2 cm, and A is a point such that OA=3 cm. There exist two circles of center A and tangent to (c). Construct these circles; calculate their radii

Given :

C) is a circle of center O and radius R=2 cm, and A is a point such that OA=3 cm.

There exist two circles of center A and tangent to (C).

To Find :

The radius of the new circles.

Solution :

Since, OA is 3 cm .

So, first circle with tangent to C if centre is at A is OA itself.

First radius, r = 3 cm.

And second circle is the on with radius , R = 3 + 2 = 5 cm.

Therefore, the radius of both the circles are 3 cm and 5 cm.

Hence, this is the required solution.

i believe the correct answer is b.