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Intermediate

The Eye of Horus

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 2r2/R2=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.

Bella

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