The crowded house

Three circles are inscribed in a rectangle. What is the area X in terms of A and B?

Scroll down for a solution to this problem.


The small circle has area X=A2/16B.

Solution by Peter Gallin.


The crowded house
Family, friends, for festivities
Season for sentiments
Around the Holy tree
With glittering lights
Love is coming down
With it’s gifts all around
The house is warm,
Winter is loud
Our hearts are not cold
All together on Xmas
The house adorned in gold


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