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Geometry - Circles 1

An article by Andy Slater with illustrations by Aris Kafantaris.

If you drew the circle yourself then you probably already know the location of the centre. But what if you're dealing with a circle on the end of some container that you saved from the kitchen waste bin?

Using a Template

A simple and often overlooked technique is to draw around your circular object onto a piece of paper. Cut out the paper circle, fold it in half, unfold and fold again at about 90° to the first fold (you don't nee to be exact). The two folds cross at the centre and you now have a paper template that you can apply to the end of your object to mark the centre.

Using Geometry

So you're, standing in a clearing in the enchanted (aren't they all?) forest. There's a circle of stones, just as the wizard told you there would be, measuring (you estimate) some 100 yards in diameter. The key to the tower in which the princess is locked, is under a rock in the centre but unfortunately there are a large number of rocks strewn about what you guess is the centre and unfortunately they are magical exploding rocks so you're quite keen that you only touch the right one. Aren't you just kicking yourself for buying up that 100 yard square of paper that the hobbit offered to sell to you three days ago? It didn't seem very useful back then did it?

The solution to this problem eluded me for quite a while before it suddenly dawned on me that the techniques for finding a right angle and bisecting a line can be employed to solve it. The method is illustrated below and while you'd probably solve the scenario above with a 345 triangle and a length of rope (surely you bought the rope?), on the terrain making bench you'll probably do it with a ruler and a set square. Either way, the technique is the same.

Geometry - Circles 1

Step 1 is to choose two points on the perimeter of the circle and draw a line between them. You'll need to find the centre of this line so you may as well choose two points at a distance that is easy to divide by two.

Step 2 is to draw a line at right angles to the centre of the first line. This new line passes through the centre of the circle.

Step 3 is to repeat step 1 with another two points on the circle.

Step 4 is to repeat step 2 to create a second line that passes through the centre of the circle. Clearly the point at which they cross is the centre of the circle. You may wish to repeat the process as a check (especially if you are dealing with exploding rocks).

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