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

# Tag: length

## 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?

## Mouth to mouth

What is the ratio of the blue and yellow lines?

## Equal rights

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

## 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?

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

## 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|.

## Wheel of fortune

A unit square and a point on the inscribed circle. What is a^{2}+b^{2}+c^{2}+d^{2}?

## The see-through triangle

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

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