Question

which of the following represents the diameter of the circle below?

image of a circle with center o, points x and y on the circle, and line segment xy passing through o

a. (overline{xy})

b. (o)

c. (x)

d. (overline{yo})

Explanation:

Step1: Recall the definition of a diameter

A diameter of a circle is a straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It is the longest chord of the circle.

Step2: Analyze each option

• Option A: $\overline{XY}$ is a line segment with endpoints \( X \) and \( Y \) on the circle, and it passes through the center \( O \) (as seen in the diagram). This fits the definition of a diameter.
• Option B: \( O \) is a point (the center of the circle), not a line segment, so it cannot be a diameter.
• Option C: \( X \) is a point on the circle, not a line segment, so it cannot be a diameter.
• Option D: $\overline{YO}$ is a line segment from \( Y \) to \( O \) (the center), which is a radius (half of the diameter), not the diameter itself.

Answer:

A. $\overline{XY}$