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Lesson Worksheet: Relationships between Chords and the Center of a Circle Mathematics

In this worksheet, we will practice identifying the relationship between chords that are equal or different in length and the center of a circle and using the properties of the chords in congruent circles to solve problems.


Suppose that 𝐵𝐶=8cm and 𝐵𝐴=7cm. Which of the following is true?

  • A𝐷𝑀>𝑋𝑌
  • B𝐷𝑀<𝑋𝑌
  • C𝐷𝑀=𝑋𝑌


Suppose that 𝐷𝐶=50cm and 𝐴𝐵=52cm. Which of the following is true?

  • A𝑀𝑋<𝑀𝑌
  • B𝑀𝑋>𝑀𝑌
  • C𝑀𝑋=𝑀𝑌


If 𝑀𝐹>𝑀𝐸, find the range of values of 𝑥 that satisfies the data represented.

  • A(20,29)
  • B(4,24)
  • C(29,62)
  • D(20,62)


Points 𝑋 and 𝑌 are midpoints of segments 𝐴𝐵 and 𝐶𝐷 respectively. If 𝐴𝐵=60, what is 𝐶𝑌?


Given that 𝐴𝐵=𝐶𝐷, 𝑀𝐶=10cm, and 𝐷𝐹=8cm, find the length of 𝑀𝐸.


Given that 𝑀 is the center of the circle, find 𝑚𝑀𝑋𝑌.


Find 𝑚𝐶.


Given that 𝑀𝐶=𝑀𝐹=3cm, 𝐴𝐶=4cm, 𝑀𝐶𝐴𝐵, and 𝑀𝐹𝐷𝐸, find the length of 𝐷𝐸.


Find 𝑚𝐵.


Given that 𝐴𝐵=𝐶𝐷=(6𝑥+3)cm, 𝑀𝐸=(3𝑥+1)cm, and 𝑀𝑂=4cm, find the length of 𝐶𝐷.

This lesson includes 19 additional questions and 207 additional question variations for subscribers.

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