Two equilateral triangles and a quarter circle that goes through both apexes. If the smaller triangle has area 1, what is the total shaded area?

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## Solution

The shaded area is 5.

First extend the quarter to a full circle. Then reflect the large triangle in the diameter as shown. The angles on the left side of B add up to 180. Therefore, DE is a straight line.

From Thales we know that angle DEC is right. Now consider triangle BEC. It is a 30-60-90 triangle, and it is well known that the short side is exactly half the hypothenuse. So |CB|=2|EB|. The large triangle is therefore four times larger than the small one.

## Visual solution

## Poem

Gizeh and it’s pyramids

Keops, Kephren, Mykerinos

So beautiful

And aesthetic

So powerfull

And dynamic

A treasure for generations

A gift for civilisations

With 1000 angles of beauty

Climbing the steps, heavenly

To the egyptian dynasty

A glorious hymn to trinity

Gizeh is eternity