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
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.
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.
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?
Question
Is a diameter a chord?
