Max Area of 2 Circles in Square of Side 1

[rudolfstr]

I've been thinking of a solution, but can't find a one. You have a square of side length 1. You have to draw 2 circles inside the square so they wouldn't go outside the square and at the same time wouldn't cross. What is the maximum area their sum can make?

 

[tiny-tim]

hi rudolfstr!

start by making a guess as to what the line joining their centres will be

(i can only think of two likely candidates)

then find where they touch the sides, and calculate their areas

(and then see if you can improve on that)

 

[Studiot]

I think Tiny-Tim's approach will work for this one, it is not as difficult as malfatti's problem, which you might find fun to look up.

There is plenty on Google.