Challenge question #42 (16/01/2017)
Junior Question
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.
To construct the new figure, arcs $l_{1}$ and $l_{2}$ have been removed from the circle, and arcs $l_{3}$ and $l_{4}$ have been added.
Senior Question
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.
Because the bridge is to be built at right angles to the river, its length is $250$ m.
If we remove the river, we have the diagram alongside.
