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## Flying purple people eater

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

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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?

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## Mouth to mouth

What is the ratio of the blue and yellow lines?

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## Equal rights

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

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## 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?

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## Carapace

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

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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|.

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## Wheel of fortune

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

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## The see-through triangle

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

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## Spike

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