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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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## Lining up half way

Show that the three red midpoints are collinear.

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## 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?

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## 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?

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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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## 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.

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