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.