To solve the given problem, we need to understand that Cynthia is standing at the center of a circular playground. In a circle, any point on the circumference is equidistant from the center of the circle.
Let's analyze the provided statements with this in mind:
A. The distance from pole 1 to pole 3 is equal to the distance from Cynthia to pole 1.
- This statement is not necessarily true because the distance between poles 1 and 3 will depend on their specific positions on the circumference and could be greater or smaller than the distance from the center to any single pole.
B. The distance from pole 1 to pole 3 is equal to the distance from pole 3 to pole 2.
- This statement is not necessarily true because the distance between poles 1 to 3 and poles 3 to 2 are not equal unless the poles are placed in such a way that they form an isosceles or equilateral triangle which is not given in the prompt.
C. The distance from Cynthia to pole 3 is equal to the distance from pole 3 to pole 2.
- This statement is not true because the distance from the center (Cynthia) to pole 3 is a radius, whereas the distance between two poles (3 and 2) could vary based on their positions around the circumference.
D. The distance from Cynthia to pole 3 is equal to the distance from Cynthia to pole 1.
- This statement is true because the distance from the center of the circle to any point on the circumference of the circle is always the same and is known as the radius. Therefore, the distance from Cynthia (the center) to pole 3 is equal to the distance from Cynthia to pole 1.
Based on the analysis above, the correct statement is:
D. The distance from Cynthia to pole 3 is equal to the distance from Cynthia to pole 1.
