Is the diameter of a circle always twice the radius?

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Is the diameter of a circle always twice the radius?

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Answer 1 · 2015-12-25T15:02:45

Yes

Explanation:

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

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

Therefore,
$A B = A O + O B = r + r = 2 r$ $AB = AO+OB = r+r = 2r$

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Is the diameter of a circle always twice the radius?

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