Categories
Intermediate

The bungee cords

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

Scroll down for a solution to this problem.

Solution

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°.

Poem

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

Bella

close

🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published.

Optionally add an image (JPEG only)