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Five Circuits, Seven Spins

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

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Pole Vaulting

Consider the mechanics of pole vaulting

Set Square

Stage: 5 Challenge Level: Challenge Level:1


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?