Categories
Intermediate

Pandora’s box

A square containing five other squares. What fraction is coloured?

Categories
Beginner

Hold the line

Two squares and two equilateral triangles. Prove the three points are collinear.

Categories
Intermediate

Another brick

A rectangle and a quarter circle. What is the area of the rectangle?

Categories
Advanced

The Common Snowdrop

A square contains a smaller square. Their vertices are cyclically connected as shown, forming four triangles. What is the minimal green area fraction?

Categories
Intermediate

The arena

In a circular arena two contestants are leaving from points A and B. Their respective speeds are such that they would collide at point C, but just before they do they exchange directions. Then they hit the edge of the arena and return to their starting points. During the whole race, A and B move […]

Categories
Intermediate

The chef’s hat

Two regular hexagons connected by a rectangle. Prove that the five vertices lie on a circle.

Categories
Intermediate

The owl of Athena

A triangle with a median and another cevian. Two areas are given. What’s the total area?

Categories
Beginner

The delta wing

A triangle with a cevian. Two lengths are given. What length is x?

Categories
Beginner

One for Pi-less Day

A quarter circle inscribed in a unit circle. What’s the orange area?

Categories
Intermediate

The Lion King

Three unit squares form the skeleton of a hexagon. What’s the area of the yellow rectangle?