Math Problem Statement

Which of the segments below is a diameter?

Solution

To solve the question "Which of the segments below is a diameter?" based on the image:

A diameter of a circle is a straight line passing through the center of the circle and touching two points on its boundary.

Key Observations:

  1. Circle with center OO: The segment OXOX clearly starts at the center OO and extends to the edge of the circle at XX, making it the diameter of the first circle.
  2. Circle with center PP: The segment BZBZ does not pass through PP (the center), so it is not the diameter of the second circle.

Correct Answer:

The correct segment that is a diameter is OXOX.

Would you like further clarification or a step-by-step explanation? Here are five related questions for further exploration:

  1. What defines the relationship between the radius and the diameter of a circle?
  2. How can you identify a diameter if the center of the circle is not explicitly marked?
  3. What is the significance of a chord, and how is it different from a diameter?
  4. Could BZBZ ever be considered a diameter in this case? Why or why not?
  5. How does understanding the properties of circles aid in solving geometry problems?

Tip: Always locate the center of the circle first when identifying a diameter!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Properties of Diameter

Formulas

Diameter = 2 × Radius

Theorems

A diameter is the longest chord in a circle and passes through the center.

Suitable Grade Level

Grades 6-8