The bungee cords

Three squares and two line segments. What’s the angle α?

Scroll down for a solution to this problem.


The angle α is 45°.

The argument rests on symmetry. First, we note that both inscribed squares are each others image under a point reflection in I followed by an appropriate scaling from that point. In particular, the square centres N and O are each others images. Thus I lies on the line segment connecting N and O.

Now from fourfold rotational symmetry we know that both N and O lie on the diagonal of the large square. Ergo, the angle α must be 45°.


Two squares are secured
With bungee cordes
Tightly fastened
Like secured luggage
We can feel attached
By a bungee rope
And never loose hope
From earth to sky diving
Like bungee jumping
Dreaming and safely falling
On the ground
There is always a friend
Holding the string


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