Question

in a plane, four circles with radii 1,3,5, and 7 are tangent to line l at the same point a, but they may be on either side of l. region s consists of all the points that lie inside exactly one of the four circles. what is the maximum possible area of region s?

Answer 1

The maximum possible area of region s can be found by creating a square inside the larger circle and calculating the difference in areas.

Step-by-step explanation:

To find the maximum possible area of region s, we need to consider the arrangement of the circles. The circles with radii 1 and 3 should be placed inside the circles with radii 5 and 7. This creates a square inside the larger circle, with side length equal to the sum of the radii of the smaller circles (1+3=4). The maximum possible area of region s is the difference between the area of the large circle and the area of the square, which is

π(7²) - (4²)

49π - 16

So, the maximum possible area of region s is 49π - 16.