You may also like

problem icon

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.

problem icon

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?

problem icon

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.