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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.

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 !!

Bella

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