Categories
Beginner

Flying purple people eater

What is the area of the purple people eater, in terms of the lengths AD and BC?

Categories
Intermediate

Mountain roads

A circular mountain peak has coordinates (0,0,3) and its base has towns C=(-4,0,0), E=( 4,0,0) on opposite sides. Town D=(0,4,0) is halfway between them, around the base. A road goes partially up and down the mountain connecting C and E. Another road connects C and D. Both roads are shortest possible. What is the ratio of the road lengths?

Categories
Beginner

Mouth to mouth

What is the ratio of the blue and yellow lines?

Categories
Beginner

Equal rights

Two squares sharing a vertex. Two vertices are connected by a line segment. What is yellow : green?

Categories
Intermediate

Holes in my heart

The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?

Categories
Beginner

Carapace

Some chords and segments inside a semicircle. What is the ratio of red to blue?

Categories
Advanced

The basketball court

An orange circle is squeezed inside a rectangle. Show that no matter how the blue point moves on the circle, the derived points Q and P will satisfy |QL| = |KP|.

Categories
Intermediate

Wheel of fortune

A unit square and a point on the inscribed circle. What is a2+b2+c2+d2?

Categories
Beginner

The see-through triangle

A regular hexagon and an equilateral triangle share a vertex. What is red : blue?

Categories
Advanced

Spike

A triangle with two line segments. What’s the angle α?