Max Area of 2 Circles in Square of Side 1

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SUMMARY

The problem of maximizing the area of two non-overlapping circles within a square of side length 1 has been discussed, with suggestions to explore the positioning of the circles. The key approach involves determining the optimal distance between the centers of the circles and calculating their respective areas based on their placement against the square's sides. Tiny-Tim's method is highlighted as a viable solution, contrasting it with the more complex Malfatti's problem, which is recommended for further exploration.

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rudolfstr
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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?
 
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hi rudolfstr! :smile:

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) :wink:
 
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.
 

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