28 Jan 2013

Math-e-Monday: Half a Triangle

Most of the questions posted so far have been about numbers, so this week we’re going to concentrate on geometry.

The people who set geometry questions in mathematics competition papers like to mess with your eyes! They are not really optical illusions but, rather like a good magician, you can’t see the whole picture because you’re concentrating only on what you’re being shown. Geometric diagrams do usually show you everything you need but not always everything you know. My advice is to redraw the diagram and fill in everything you know that is related to the question; it could be trigonometry or circle theorems or construction techniques. Then make sure you read the question carefully to check for details that are written down but not illustrated in the given diagram.

Lastly, brush up on some of the more obscure geometric theorems. You can always prove things from first principles, but in a maths test that wastes precious time. It is better to be prepared with a basket full of theorems and then figure out which ones you need.

The Question

The diagram above shows a circle centre C (not drawn to scale). The line CQ is perpendicular to the diameter PR. The triangle PQR has double the area of triangle PSR. Find the angle PRS.

This is not a PMQ so feel free to discuss this puzzle in the comments section below.

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