Categories
Intermediate

Under the dome

Two semicircles with four squares and a yellow rectangle. What is the aspect ratio of the latter?

Categories
Intermediate

Antennas above and below

The triangle ABC has orthocentre H, so that HA is an antenna above the green hill. The rectangle BCDE is inscribed in the circumcircle (ABC). Show that HA = CD = BE.

Categories
Advanced

Squaring a rectangle II

A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.

Categories
Intermediate

Wings

Two wings are attached to the corner of a rectangle, and have corners lined up with the diagonal of the rectangle. The angles at the lower wing tips are equal. Must α = β at the left wing tips?

Categories
Intermediate

No laughing matter

Two squares share a vertex. Each square contains a coloured rectangle with extended side. What’s green : blue? By Matthew Arcus.

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?