Categories
Intermediate

Playing fields

Show equality of the green and orange square playing field areas.

Categories
Beginner

The punctured hexagon

A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.

Categories
Intermediate

Vanishing point II

Six squares and four coloured triangles. What is red : blue : yellow : green?

Categories
Intermediate

Balancing act II

Two squares share a vertex. What’s the angle α?

Categories
Advanced

Alien eye

Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)

Categories
Intermediate

Pop you bubble

A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.

Categories
Advanced

The ceiling lamp

A regular octagon with two diagonals and a square. Prove that the four red points are concyclic.

Categories
Beginner

Stay centred

Two squares share a vertex. Prove that the red point is the circumcentre of the red triangle.

Categories
Advanced

Peeping out II

A unit square and a rectangle touching three square sides and passing through the midpoint of the upper side. What is the minimal blue area?

Categories
Beginner

Peeping out

A unit square and a rectangle. What is the blue area?