Categories
Intermediate

Mind the steps

Three similar rectangles and a line segment. Express red in terms of blue and green.

Categories
Intermediate

In times out

What is the area of the green rectangle, which has sides tangent to the incircle and circumcircle of a triangle with side lengths a, b, c.? (Write the answer as a multiple of a quotient of two elementary symmetric functions in a, b, c.)

Categories
Intermediate

Four six four

A regular hexagon and two similar rectangles. What fraction is green?

Categories
Intermediate

Six four

A regular hexagon and an inscribed tilted rectangle. What is the angle α?

Categories
Beginner

Domino day II

Two large congruent rectangles share a vertex and contain two coloured rectangles. What is red : blue?

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?

Categories
Intermediate

Uneven brickwork

A rectangle is divided into six rectangles of equal area. What fraction is green?

Categories
Beginner

Between the lines II

Two rectangles are at right angles and have equal area. Prove that the three black lines are parallel.

Categories
Beginner

A golden year

Two squares, a rectangle and a semicircle. What is yellow : green?