The headphones

A unit square, a semicircle, a right triangle and an isosceles triangle. What is the total purple area?

Scroll down for a solution to this problem.


The purple area is 1/2.

Solution by Dr. StranGe.

The reason why the isosceles triangle is congruent with the right isosceles one is that there is only one unique isosceles possible (intersect the perpendicular bisector of the top angle with the circle).

Visual solution

Proof without words by David Andriana.


Headphones on my ears
Just two big flies so clear
Helping to escape
In music and poetry
The more of me I hear
I feel the words and notes
Looking in the moon
Getting my dreams soon
Singing this melody
Sharp or soft, always gently
Headph. are good connection
For experimentation


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