2021 AMC 10B Problems/Problem 7
Problem
In a plane, four circles with radii 
and 
are tangent to line 
at the same point 
but they may be on either side of . Region 
consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region ?
Solution
[asy]
pair A=(10,0);
pair B=(-10,0);
draw(A--B);
draw(circle((0,-1),1));
draw(circle((0,-3),3));
draw(circle((0,-5),5));
draw(circle((0,7),7));
dot((0,7));
draw((0,7)--(0,0));
label("",(0,3.5),E);
label("",(-9,0),S);
[/asy]
After a bit of wishful thinking and inspection, we find that the above configuration maximizes our area. 
