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Lawnmower

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

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Quads

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?

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Bi-cyclics

Two circles intersect at A and B. Points C and D move round one circle. CA and DB cut the other circle at E and F. What do you notice about the line segments CD and EF?

Floating in Space

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

You might consider joining corresponding points. Do you recognise the resulting quadrilaterals? If you do you will need to prove they are what they seem to be.

Why not make some assumptions such as AB = XY as this would not affect the fact that the lines are parallel.