### Darts and Kites

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

### 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?

### 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:

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.