Challenge Question

Challenge question #42 (16/01/2017)

Junior Question

Maths Image Suppose you are given the circle alongside.

Show how to construct a figure which has the same perimeter as the circle, and the same area as the square inscribed inside the circle.

Senior Question

Maths Image A factory, F, and a railway station, R, are seperated by a $250$ m wide river. A road and a bridge need to be constructed to transport products between the two places.

F is $4$ km north of R, F is $2$ km from the river, R is $1$ km from the river, and the bridge must cross the river at right-angles. Determine the shortest possible length of road and bridge required to join the factory to the railway station.

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