Let's analyze the problem step-by-step based on the scenario provided:
1. Position of Cynthia: Cynthia is standing at the center of a circular playground.
2. Poles on Circumference: There are three poles, pole 1, pole 2, and pole 3, positioned on the circumference of the circle.
### Determine Distances:
- The distance from Cynthia to any of the poles (pole 1, pole 2, or pole 3) is the radius of the circle, as Cynthia is at the center and the poles are on the circumference.
### Analysis of Statements:
Statement A:
- The distance from pole 1 to pole 3 is equal to the distance from Cynthia to pole 1.
- The distance from Cynthia to pole 1 is the radius of the circle.
- The distance between pole 1 and pole 3 is a chord length, not necessarily equal to the radius.
- Conclusion: This statement is incorrect because a chord length in a circle isn't generally equal to the radius.
Statement B:
- The distance from pole 1 to pole 3 is equal to the distance from pole 3 to pole 2.
- For this to be true, poles 1, 2, and 3 would need to form an equilateral triangle, where all sides are equal.
- No specific information is given to assume that poles 1, 2, and 3 form an equilateral triangle.
- Conclusion: This statement cannot be considered true as it requires a condition not provided in the problem.
Statement C:
- The distance from Cynthia to pole 3 is equal to the distance from pole 3 to pole 2.
- Again, the distance from Cynthia to any pole is the radius of the circle.
- The distance between pole 3 and pole 2 is a chord length, which is not necessarily equal to the radius.
- Conclusion: This statement is also incorrect because a chord length in a circle is generally not equal to the radius.
### Conclusion:
- After analyzing all the statements, none of the given statements (A, B, or C) is universally true based on the given information.
Therefore, there is no specified statement that can be generalized as true in this context.
