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Ruyles squares

There are four possible squares with a vertex at distance a from the centre and two vertices on the circle of radius r. Find their areas in terms of a and r.

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Solution

The square areas are (r2+a2±√(6r2a2-r4-a4))/2.

Solution by @chlewey@col.social.

Poem

Ruyles squares
Recessed windows
Various colours
Like church stained glass
Eyes open to the world
That filters the light
Tiles that contribute to beauty
Of geometry
Hand in hand
Heart to heart
The squares of hapiness

Bella

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