First, lets just look at the figure on the left with a single circle and four circles inscribed in it. Let be the area of the larger circle (with radius ) and be the area of each of the smaller circles (with radius ). You are looking for the following ratio: which is . So you essentially need to find the ratio of the radii.
Put a coordinate system on your circle picture, with the center of the large, original circle at the origin.
Look at the smaller circle in quadrant I of the coordinate system. It touches both the x-axis and the y-axis. Therefore, its center is at (r,r). Using this, you can calculate the distance from the origin to its center as and if you go from the center to the point of tangency (adding an r from this point) you will have gone R. This means . Solving for r, you can see .
Plug this in the original question and you will find
Can you use this information to figure out the answer to your question?