Circle Theorem Gets an Art Attack
An unexpected use for a bit of GCSE maths
01 September 2025
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.
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.
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.