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Circle Theorem Gets an Art Attack

An unexpected use for a bit of GCSE maths


People of a certain vintage will remember a children's art programme from the 1990s called Art Attack, hosted by Neil Buchanan.  It was a joyful programme that treated children as grown-ups, in the spirit of the great Tony Hart.

In one episode, Buchanan used a dinner plate to draw a circle on a piece of stiff board.  "Now we just need to find the centre of the circle," he said.

But how?  Usually you use a compass to draw a circle and so you know exactly where the centre is.  But if you use a plate, there's nothing to indicate where the centre is.

Before you read on, you might like to spend a moment thinking about how YOU would find the centre at this point.

Art Attack

OK, here is what Buchanan did. First he took a piece of A4 paper and placed it so that one corner touched the circle.  He then marked off the two points where the paper crossed the circle, and took a ruler to join those points with a straight line.  He then placed the paper in a different orientation and drew a second line.  Where the two lines joined was the centre.

Art Attack

There was no fanfare and no explanation, but what Buchanan had done (without necessarily knowing it) was reverse-engineer a bit of GCSE maths known as Thales Theorem, which says that a triangle inscribed in a semicircle will always have a right-angle.

And to think there are people who reckon circle theorems have no relevance to the real world.