The hot-air balloon

Two circles, four tangent line segments and a square. What’s the proportion red : blue?

Scroll down for a solution to this problem.


The proportion red : blue is 25 : 1.

Solution by Matthew Arcus.

As is clear from this solution, the tangents to the red circle are superfluous. This is explicitly shown in the solution below.

Solution by Dr Rick.


The hot air balloon
Flies all around the year
He is the king in the air
You’ll have fun, this day is the one
Up in the air you’ll fly
We will see you passing by
You’ll go from south to west
The currents will keep you best
Safely go down and land
You’ll say for sure do it again !


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