The longest chord
The diameter is the longest chord
Short and long
A chord of a circle can be short or long. Imagine sliding a chord towards the centre, and then away from it.
Which chord of a circle is the longest?
What this lesson covers
The idea
The chord nearest the centre is the one containing the centre, at distance zero, so the diameter is the greatest chord of a circle.
Short and long
A chord of a circle can be short or long. Imagine sliding a chord towards the centre, and then away from it.
Which chord of a circle is the longest?
- A chord through the centre
- A chord near the edge
- Every chord is about the same
Find the longest
Touch the circle to slide a chord. Find the longest chord you can, then push the chord out to the edge.
Nearest is longest
The chord nearest the centre is the one that contains the centre, at distance zero. So the diameter is the greatest chord of a circle.
The nearer a chord is to the centre, the longer it is. The nearest it can be is distance 0: a chord through the centre, which is a diameter. If you push a chord away from the centre, it shrinks to a single point, with length zero. That point is at a distance equal to the radius.
Notes
The chord nearest the centre is the diameter, at distance zero, so the diameter is the greatest chord of a circle.
Check yourself
A circle has radius 6 cm. What is the length of its longest chord, in cm?
Answer: 12 cm
The longest chord is a diameter, and a diameter is twice the radius: 2 × 6 = 12 cm.
Which chord of a circle is the longest?
A circle has radius 5 cm. Can it have a chord that is 11 cm long?
A circle has radius 5 cm. A chord is pushed out from the centre until it becomes a single point on the circle. How far is that point from the centre, in cm?
Answer: 5 cm
The point is on the circle, so it is a radius away from the centre: 5 cm.
- A chord 1 cm from the centre. A diameter is at distance 0, which is nearer, so a diameter is longer.
- A chord close to the edge. Chords near the edge are the shortest, because they are far from the centre.
- A diameter — correct. Yes. It is at distance zero from the centre, the nearest a chord can be.
- No, no chord is longer than the diameter, 10 cm — correct. Yes. The diameter is the greatest chord, and here it is 10 cm.
- Yes, a chord very close to the centre. The chord closest to the centre is the diameter, which is only 10 cm long.
- Yes, a chord very close to the edge. Chords near the edge are short. The longest chord is the 10 cm diameter.