Parts of a Circle — Radius, Diameter and Chord

The Story

Ms. Rao stuck a pin in the centre of a paper circle and tied a piece of string from the pin to the edge. "Walk the string around the rim," she told Kabir, "and tell me if it changes length."

Kabir traced the string all the way around, keeping the pin end fixed. "It's the same the whole way. It never gets longer or shorter."

"That's the definition of a circle," said Ms. Rao. "Every point on the rim is the exact same distance from the centre. That fixed distance — pin to rim — is the radius."

She then had Anaya draw a straight line from one side of the rim, through the centre pin, to the opposite side. "What do you notice?"

Anaya measured it against Kabir's string. "It's exactly twice as long as the radius."

"That full line through the centre, touching the circle on both sides, is the diameter," said Ms. Rao. "And you've just found the relationship yourself: diameter equals two times the radius. Always, for any circle, any size."

Kabir tried the reverse: "So if I only know the diameter, I halve it to get the radius?"

"Exactly."

Then Ms. Rao drew a line from one point on the rim to another point on the rim — but this time NOT through the centre. "This is also a straight line touching the circle at two points. Is it a diameter?"

Anaya compared it to the true diameter. "It's shorter. It doesn't go through the pin."

"Right — any straight line joining two points on the circle is a chord. The diameter is actually a special chord — the longest one possible, because it's the only one that passes through the centre. Every diameter is a chord, but most chords are not diameters."

She finished by tracing the whole rim itself with a coloured pen. "And the boundary of the circle — the curved path itself — is the circumference. Not a straight measurement like the others, but the distance if you walked all the way around the edge."

Kabir summed it up in his notebook: centre, radius, diameter, chord, circumference — one drawing, five names, each one describing a different part of exactly the same shape.