One for Pi-less Day

A quarter circle inscribed in a unit circle. What’s the orange area?

Scroll down for a solution to this problem.


The orange area is 1.

Since it’s a quarter circle, the angle between the radii is right. From Thales we know that the line connecting the end points of those radii must be a diagonal of the unit circle. Using the Pythagorean theorem, we can find the radius to be √2.

The orange area is half unit circle – (quarter circle – the triangle) = π/2-(π/2-1)=1.


An orange quarter of moon
That comes out very soon
The moon is orange and glowed
It looks like fire that burned
Playing and hiding with the clouds
The moon is a quarter, not perfectly round
All the days passes so easy
The orange moon makes me happy !!


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