Categories
Beginner

The dangling square

Four squares and five shared vertices. If the orange area is 4, what is the green area?

Categories
Beginner

The yellow sailboat

A square, two equilateral triangles and an extended side. What is the proportion yellow : blue?

Categories
Beginner

Mondriaan II

A square contains three squares (black sides), one of which has an extended side (blue). What is the proportion yellow : blue?

Categories
Intermediate

Warning triangle II

A square, a triangle and two equal angles. What is the angle α?

Categories
Advanced

The green quad

Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral?

Categories
Intermediate

The strawberry ice cream

Two tangent circles and a triangle. The figure has reflection symmetry in the vertical diameter d, of which one ninth is above the horizontal chord. What fraction is pink?

Categories
Beginner

Seventies tipi II

A triangle containing two tangent semicircles. What’s the proportion α : β?

Categories
Beginner

The inner sanctum

A square with four congruent equilateral triangles. What fraction is yellow?

Categories
Intermediate

The colour purple

A rectangle is split by two perpendicular lines. The four circles pass through vertices and intersection points. Their centres form a purple quadrilateral. What fraction of the large rectangle area does it cover?

Categories
Advanced

Triangle quartet II

Three coloured equilateral triangles share three vertices. Prove that the triangle formed by their centres is also equilateral.