The distance between the centers of the two circles is zero, making them concentric circles. The length of the tangent from a point on the larger circle to the smaller circle is the square root of the difference of their radii squared, so 4 equals the square root of (5r squared minus r squared). Squaring both sides gives 16 equals 4r squared, meaning the radius of the smaller circle is r equals 2 and the radius of the larger circle is the square root of 20. The area between the circles is found by subtracting the smaller area from the larger area, yielding pi times (20 minus 4), which equals 16 pi.