The tumble dryer

Today’s Catriona Shearer puzzle.

18.
The Tumble Dryer

What fraction of the big square is shaded?

Spoiler!

The squares look chaotic but three of them have parallel edges and two contact the circle at two corners; that means the perpendicular bisectors of the edges connecting those corners intersect the circle’s center, and since the squares’ edges are parallel the centers of the circle and those two squares must be colinear. Therefore, if these are unit squares, the contact points are the corners of a 3 by 1 rectangle inscribed inside the circle.

Then the diameter of the circle is the diagonal of that rectangle, whose length is . Which also is the length of a side of the big square.

The big square’s area is and the squares add up to , so the answer is .