The bear trap

A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?

Scroll down for a solution to this problem.


The semicircle area is πba2/(4a-2b).

Solution by Carlos Eŭgenĭo Thompson Pinzón.


The bear trap is closing
On the unleashed bear
He makes war
Without mercy
He bombs
He deports
He kills
He is absolutely cruel
He razes cities and villages
But on the other side
The people under attack
Are brave
Motivated fighters
They will win
The bear is trapped
He will loose


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