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Eye of the apple

A circle with an inscribed triangle with an inscribed circle. The centre of the large circle is on the small one. What fraction of the area is blue?

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Solution

The blue fraction is 3-2√2.

Solution by ʙᴇɴᴇ.

The intermediate result that d2=R2-2Rr is known as Euler’s theorem.

Poem

Eye of the apple
It could be also the apple of my eye
Cherishing someone we love
So precious
So rare
And somebody we like and care
He cares for me
When I’m in need or in pain
Already when the days starts
You are the apple of my eye
Always in my heart
Nothing can keep us apart

Bella

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