Circles
44. The Radius Rule · always equal, always from centre to edge
All segments from the centre to the circumference are equal in length.
A radius is a line segment from the centre O to any point on the circle. All radii of the same circle are equal in length. The plural is "radii".
What this lesson covers
Try to break it
Try dragging each point. Notice how the lines OP, OA, and OB always stay the same length, no matter where they point!
How you build it
Draw a circle and three radii.
- Mark the centre point O.
- With centre O, draw the circle.
- Mark point P on the circle.
- Mark point A on the circle.
- Mark point B on the circle.
- Join centre O to P — this is a radius.
- Join centre O to A — another radius.
- Join centre O to B — every radius of a circle has the same length.
The proof, step by step
Prove that every radius of the circle has the same length.
- The radius is defined as the segment from the centre to the circumference.
- Drag points P, A, and B around the circle.
- Observe that OP, OA, and OB always remain equal in length.
- This confirms that every radius of a circle is equal to every other radius.
Worked example
In a circle with centre O, a line segment connects O to a point on the circumference. If the length of this segment is 9 cm, what is the radius of the circle?
By definition, the radius is the line segment joining the centre to any point on the circumference. Since this segment is given as 9 cm, the radius is exactly 9 cm.
- 4.5 cm
- 9 cm — correct
- 18 cm
- 72 cm