True or false:
The radius of a circle is the chord.
To solve this question, we must understand the definitions of the terms "radius" and "chord" in the context of a circle:
- A radius is a line segment that connects the center of the circle to any point on the circle's circumference. All radii of a circle are equal in length.
- A chord is a line segment whose endpoints both lie on the circle's circumference. The chord does not necessarily pass through the center of the circle, and chords can have different lengths.
Given these definitions, observe the following points:
- The radius is inherently different from the general concept of a chord because the radius must include the circle's center as one of its points, while a chord only specifies that both endpoints lie on the circle's edge, offering no requirement to pass through the center.
- An important sub-case is the diameter, which is a special chord that does pass through the center and is equal to twice the radius (2r). However, while the diameter is indeed a chord, the radius itself cannot be viewed as such because it does not completely lie between two points on the circle but instead starts from the center.
Hence, the statement that "The radius of a circle is the chord" is false because a radius does not fulfill the general definition of a chord, which requires two endpoints on the circle's circumference that do not include the center of the circle.
Therefore, the correct choice is False.