Question

which line segment is a diameter of circle l?

• $overline{jl}$
• $overline{hk}$
• $overline{gk}$
• $overline{il}$

Explanation:

A diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circle. Looking at circle \(L\):

• \(\overline{JL}\): Only one endpoint (\(J\)) is on the circle; \(L\) is the center, so this is a radius, not a diameter.
• \(\overline{HK}\): This segment passes through the center \(L\), with both endpoints \(H\) and \(K\) on the circle, so it meets the definition of a diameter.
• \(\overline{GK}\): This segment connects two points on the circle but does not pass through the center \(L\), so it is a chord, not a diameter.
• \(\overline{IL}\): Only one endpoint (\(I\)) is on the circle; \(L\) is the center, so this is a radius, not a diameter.

Answer:

○ \(\overline{HK}\)