A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?
The dark lord
Two congruent equilateral triangles and two squares. What’s the angle α?
The pointy shoe
A quarter circle, a semicircle and a triangle. What’s the angle α?
Cordon sanitaire
Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.
The green zone
A quarter circle and a right triangle inside a square. One of the vertices of the triangle is the square’s centre. What fraction of the square’s area is green?
The open book
Three squares share four vertices. What is the proportion of the line segment lengths a and b?
The kissing circles
A rectangle with three touching quarter circles. What fraction of its area is coloured?
The balancing act
A square with two perpendicular lines. What is the minimal blue fraction?
The commons
Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?
Softening the edges
A quarter circle contains a semicircle and a square. What fraction of the area is purple?