Always, Sometimes, Never

The relationship between chords and diameters can be a little tricky. Sometimes they're one and the same, and sometimes they're not. See if you can figure out the difference by studying the examples below.

Example 1

Example 2

Example 3

circle

In this circle, is $\small\mathsf{ \overline {FG}}$ a chord or a diameter?

$\small\mathsf{ \overline {FG}}$ is a chord because both endpoints are on the circle. $\small\mathsf{ \overline {FG}}$ is also a diameter because it is a chord that goes through the center of the circle.

circle

In this circle, is $\small\mathsf{ \overline {LM}}$ a chord or a diameter?

$\small\mathsf{ \overline {LM}}$ is a chord because both endpoints are on the circle. $\small\mathsf{ \overline {LM}}$ does not go through the center, so it is not a diameter.

In other words, $\small\mathsf{ \overline {LM}}$ is a chord that isn't a diameter.

circle

In the following circle, is $\small\mathsf{ \overline {LM}}$ a chord or a diameter?

$\small\mathsf{ \overline {LM}}$ is a chord and a diameter. Its endpoints are on the circle, and it goes through the center of the circle.

Question

Is a chord a diameter?

A chord is sometimes a diameter, and sometimes not.

Question

Is a diameter a chord?

A diameter is always a chord. Every diameter is a line segment with endpoints on circle.

Is a chord a diameter, or is a diameter a chord?

Question

Question