Question

Is the diameter of a circle always twice the radius?

Answer 1

Yes

Explanation:

Diameter `AB` of a circle with center `O` connects two points on the circle (`A` and `B`) and passes through a center (point `O`). Therefore, it is a sum of two segments - from a point on a circle to a center (`AO`) and from a center to another point on a circle (`OB`):
`AB=AO+OB`

Since a circle is a locus of all points equidistant from a center (and the distance is called the radius of a circle - `r`),
`AO=r` and `OB=r`.

Therefore,
`AB = AO+OB = r+r = 2r`