Circles
45. The Diameter's Path · Always through the center, always double the radius
AB always passes through center O with ends on the circle.
A diameter is a chord that passes through the centre O of the circle. It is the longest chord and is exactly twice the radius: AB = 2 · r. A circle has infinitely many diameters; all are equal in length.
What this lesson covers
Try to break it
Try dragging A around the circle. The line AB always passes through the center O. Can you make it miss the center? No matter how you move A, B moves to the opposite side, so the line stays a diameter. A diameter must always go through the center.
How you build it
Draw a diameter through the centre.
- Mark the centre point O near the middle of the canvas.
- With centre O, draw the circle.
- Mark a point A anywhere on the circle.
- Draw a straight line through A and O. Extended, it meets the circle again at the opposite point B — AB is the diameter.
The proof, step by step
By definition, a diameter connects two points on the circle and passes through the center. Drag A to verify this is always true!
- A chord is a straight segment joining two points on the circle.
- The diameter is a chord that passes through the centre O.
- The centre O is the midpoint of the diameter, so OA and OB are both radii.
- Therefore the diameter AB = OA + OB = 2 × radius.
Worked example
The diameter of a circle is always _______ its radius.
Diameter = 2 × Radius. So the diameter is always double the radius.
- half of
- equal to
- double — correct
- triple