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

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## Solution

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.

## Poem

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 !!