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Darts and Kites

Explore the geometry of these dart and kite shapes!

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Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

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Rhombus in Rectangle

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

Center Path

Stage: 3 and 4 Challenge Level: Challenge Level:1

Ask yourself "is there anything special about the angle between the diagonals of a rhombus?'' Now think again about the path of X as the linkage moves.

This problem was at first a "tough nut'' to crack! A friend of mine calls these sort of questions, where no-one can find a solution for quite a long while, 'Mars Bar question'. Perhaps your teacher or your Mum will buy you a Mars Bar if you can solve this.