Colour confinement

A semicircle with three tangent line segments. What is its area in terms of lengths a and b?

Scroll down for a solution to this problem.


The purple area is πab/2.

Solution by Fernando Gutiérrez.

Visual solution

Solution without words by David Andriana.


Colour confinement
What happened to me
In a ½ cercle I’ll be
I’am a ½ disk so nice
And can also be twice
Well known as arbelos or amphitheatre
Here I’m purple
Just to stay in the circle
Some say I’m a mystery
Here I live in majesty
Confined in my shelter
Tomorrow I’ll be free


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