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 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
Beginner

The stained glass

Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?

Categories
Intermediate

The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

Categories
Advanced

The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

Categories
Beginner

The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

Categories
Intermediate

Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

Categories
Advanced

The bigger picture

In a small square two perpendicular lines are drawn. A larger parallel square is constructed as shown. Prove it is a scaled copy of the smaller square but rotated 90° anticlockwise.

Categories
Intermediate

La Flèche Wallonne

A triangle is divided in four. What is the black area?

Categories
Intermediate

The attic room

A blue square is topped with a right triangle. Using line segments to the top, a green quadrilateral is constructed with at least two right angles. What is the area proportion green : blue?