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Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Pole Vaulting

Consider the mechanics of pole vaulting

Five Circuits, Seven Spins

Age 16 to 18 Challenge Level:

To find the dimensions of the tray you need to work out the angle through which the plate turns in one circuit and from that the length of its circumference that comes into contact with the edge of the tray as the plate rolls round.

You will need to use algebra to label the lengths of the side of the tray.