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.

Solution

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

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

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. https://t.co/ez7OdY7bOc Inspired by @bruyle1 pic.twitter.com/W2z2QTrJyB

— Mirangu (@Mirangu1) December 15, 2022