Circles
46. The Chord Connection · joining any two points on the circle
PQ is always a chord because P and Q stay on the circle.
A chord is a line segment whose two endpoints both lie on the circle. Drag P or Q anywhere on the circle — PQ remains a chord. The longest possible chord passes through the centre and is called the diameter.
What this lesson covers
Try to break it
What if I move P and Q closer? The chord gets shorter. What if they are opposite? It becomes a diameter!
How you build it
Draw a chord on a circle.
- Draw a circle.
- Mark point A on the circle.
- Mark point B on the circle.
- Join A and B to draw the chord — both endpoints lie on the circle.
The proof, step by step
Prove that PQ is a chord — both its endpoints lie on the circle.
- A chord must have both endpoints on the circle's circumference.
- A diameter is a special chord that passes through the center.
- Not every line segment inside a circle is a chord; endpoints must touch the circle.
Worked example
In the given circle with centre O, which of the following line segments is a chord?
By definition, a chord is a straight line segment joining any two points on the circumference of a circle. Option 2 correctly describes this property.
- A segment with one endpoint inside and one outside the circle
- A segment with both endpoints on the circumference — correct
- A segment connecting the centre to a point on the circumference
- A curved line along the edge of the circle