Cherry picking

Two quarter circles and a red circle tangent to two chords. What fraction is red?

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The red fraction is 4(16-5√7)/81, which approximates to 13,7%.

Solution by ricardpe.


Cherry picking
When we sing about cherry time
And gay nightingales and mocking blackbirds
Will all be celebrating …….
But it is very short
The cherry season
Coral earrings
And drops of blood
That we pick while dreaming

(French song, le temps des cerises, 1866)


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