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

# Author: Marshall W. Buck

## 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?

## Lining up half way

Show that the three red midpoints are collinear.

## Running man

What is the area of the coloured figure? Can you determine the area without counting the number of squares in each different-coloured shape?

## Baby steps

The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?

## 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?

## Three dome home

How does the white area inside the big semicircle compare to the combined white areas of the 3 smaller semicircles below it? Equally coloured semicircles are congruent.

## 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|.