A semicircle containing two equilateral triangles containing a circle. What fraction is blue?

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## Solution

The blue fraction is 3/8.

First, establish that the side length of the equilateral triangles equals the radius of the semicircle, because its centre must be the upper common vertex that is equidistant from three points on it.

Now draw the altitude through the small circle’s centre as shown. It is well known that in an equilateral triangle it’s height is √3/2 times the side length. We thus have 2r=√3R/2, and hence 2r^{2}/R^{2}=3/8.

## Poem

The eye of Horus

An eye for well-being

An eye for care and healing

An eye filled with gazelle’s milk

As beautiful and soft as silk

For most people it has a special meaning

Like giving or offering

The right eye is the Sun

The left eye is the Moon

And in the Sky the King.