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We have Edwin Taylor, age 18 of the Leventhorpe School, Sawbridgeworth, to thank for the following solution.
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
Can you make a tetrahedron whose faces all have the same perimeter?