Question

cynthia is standing at the center of a circular playground. which statement is true with respect to cynthias position?
a. the distance from pole 1 to pole 3 is equal to the distance from cynthia to pole 1.
b. the distance from pole 1 to pole 3 is equal to the distance from pole 3 to pole 2.
c. the distance from cynthia to pole 3 is equal to the distance from pole 3 to pole 2.
d. the distance from cynthia to pole 3 is equal to the distance from cynthia to pole 1.

Explanation:

Step1: Recall the property of a circle

In a circle, the distance from the center to any point on the circle (radius) is equal.

Step2: Analyze each option

• Option A: The distance from pole 1 to pole 3 is a chord length, and the distance from Cynthia (center) to pole 1 is a radius. Chord length is not equal to radius (except when chord is diameter).
• Option B: There is no information given to suggest that the arc lengths (and thus chord lengths) between pole 1 - pole 3 and pole 3 - pole 2 are equal.
• Option C: The distance from Cynthia (center) to pole 3 is a radius, and the distance from pole 3 to pole 2 is a chord length. They are not equal.
• Option D: Since Cynthia is at the center and pole 1 and pole 3 are on the circular playground (i.e., on the circle), by the definition of a circle, the distance from the center (Cynthia) to any point on the circle (pole 1 and pole 3) is equal (both are radii).

Answer:

D. The distance from Cynthia to pole 3 is equal to the distance from Cynthia to pole 1.