Question

question 44 of 44 which of the following is represented by (overline{mn})? image of a circle with center m and point n on the circle
a. diameter of the circle
b. a chord of the circle
c. radius of the circle
d. circumference of the circle

Explanation:

To determine what \(\overline{MN}\) represents, we analyze each option:

• Option A: A diameter is a chord passing through the center, with length twice the radius. \(\overline{MN}\) has one endpoint at the center (\(M\)) and one on the circle (\(N\)), so it is not a diameter (a diameter would have both endpoints on the circle and pass through the center, e.g., a segment like \(\overline{NP}\) where \(P\) is another point on the circle opposite \(N\) through \(M\)).
• Option B: A chord is a segment with both endpoints on the circle. Since \(M\) is the center (not on the circle’s edge, but the center), \(\overline{MN}\) does not have both endpoints on the circle, so it is not a chord.
• Option C: The radius of a circle is a segment from the center to any point on the circle. Here, \(M\) is the center, and \(N\) is on the circle, so \(\overline{MN}\) fits the definition of a radius.
• Option D: The circumference is the total length of the circle’s edge (a curve), not a line segment. \(\overline{MN}\) is a segment, so it cannot be the circumference.

Answer:

C. Radius of the circle