A thread on the wheel
Chord and diameter
A thread on a wheel
Tie a thread tight between two points of a wheel. The thread runs straight from one point of the circle to another. Now imagine joining both ends of the thread to the centre of the wheel.
What shape do the thread and the two joins make?
What this lesson covers
The idea
A line segment joining two points of a circle is a chord, which subtends an angle at the centre formed by joining its end points to the centre; a chord through the centre is a diameter.
A thread on a wheel
Tie a thread tight between two points of a wheel. The thread runs straight from one point of the circle to another. Now imagine joining both ends of the thread to the centre of the wheel.
What shape do the thread and the two joins make?
- A triangle
- A square
- Another circle
Move the thread
A is the centre. The thread BC joins two points B and C of the circle. Drag B and C round the edge.
Chord and diameter
A line segment joining two points of a circle is a chord. It subtends an angle at the centre: join its end points to the centre. A chord that passes through the centre is a diameter.
BC is a chord and ∠BAC is the angle it subtends at the centre A. DE passes through A, so DE is a diameter.
Notes
A chord joins two points of a circle and subtends an angle at the centre. A chord through the centre is a diameter.
Check yourself
What is a diameter of a circle?
PQ is a chord of a circle with centre O. Which angle does PQ subtend at the centre?
AB is a diameter of a circle with centre O. What is ∠AOB, in degrees?
Answer: 180 °
OA and OB lie along the same line, pointing opposite ways. The angle between them is a straight angle: 180°.
Which statement is true?
- Any chord of the circle. Every diameter is a chord, but a chord need not pass through the centre.
- A line from the centre to a point on the circle. That one is a radius. A diameter joins two points of the circle, through the centre.
- A chord that passes through the centre — correct. Yes. It joins two points of the circle and goes through the centre.
- ∠POQ — correct. Yes. Join P and Q to the centre O, and the angle between OP and OQ is the one the chord subtends.
- ∠OPQ. That angle is at P, on the circle. The angle subtended at the centre is at O.
- ∠PQO. That angle is at Q, on the circle. The angle subtended at the centre is at O.
- Every chord is a diameter. A chord that does not pass through the centre is not a diameter.
- Every diameter is a chord — correct. Yes. A diameter joins two points of the circle, so it is a chord (one that goes through the centre).
- A chord is always shorter than the radius. A chord can be long. A diameter is a chord, and it is twice the radius.