Question

6 in which of the following circles is the line segment a diameter? a b c d e

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.

Step2: Analyze each option

• Option A: The line segment is a chord but does not pass through the center (it's a horizontal chord near the top), so not a diameter.
• Option B: The line is a secant (extends beyond the circle) and the segment shown does not have both endpoints on the circle (or pass through the center properly), so not a diameter.
• Option C: The line segment passes through the center of the circle and its endpoints lie on the circle, so this satisfies the definition of a diameter.
• Option D: The line is a tangent (touches the circle at one point), so there is no segment with two endpoints on the circle here, not a diameter.
• Option E: The line segment is a radius (from center to circumference), not a diameter.

Answer:

C. The line segment in circle C passes through the center and has endpoints on the circle, satisfying the definition of a diameter.