Categories
Intermediate

Hidden parallelogram

Blue circle (ACDGB) with CEG || AB. Pink circle (EDG) intersects AB at I. Extend DI to intersect blue circle at J, then JC intersects AB at M. Show that IM = CE.

Categories
Advanced

Double eclipse

Given green and blue discs, construct a red region so that for every ray leaving L stays in the blue region exactly as long as it does in the pink region. (Namely, KM = OL.)

Categories
Advanced

Pentagon pleasure

Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?

Categories
Intermediate

Under the dome

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

Categories
Intermediate

Pull the string

Two regular hexagons and a circumcircle. What is blue : red?

Categories
Beginner

Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

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

Crashing the kite

The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?

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

Sticky corners

Two equilateral triangles and several line segments. What is red : yellow?