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Lesson Worksheet: Parallel Chords and Tangents in a Circle Mathematics

In this worksheet, we will practice using the parallel chords and the parallel tangents and chords of a circle to deduce the equal measures of the arcs between them and find missing lengths or angles.


In the given figure, the measure of 𝐴𝐵=62, the measure of 𝐵𝐶=110, and the measure of 𝐴𝐷=126. What can we conclude about 𝐴𝐷 and 𝐵𝐶?

  • AThey are the same length.
  • BThey are parallel.
  • CThey are parallel and of the same length.
  • DThey are perpendicular.
  • EThey are neither parallel nor perpendicular.


In which of these figures will 𝐴𝐵 be parallel to 𝐶𝐷?

  • A
  • B
  • C
  • D
  • E


In the given figure, if the measure of arc 𝐵𝐷=65, find the measure of arc 𝐶𝐷.


Find 𝑚𝐵𝐸 where 𝑀 is the center of the circle.


In the following figure, a rectangle 𝐴𝐵𝐶𝐷 is inscribed in a circle, where the measure of 𝐴𝐵=71. Find the measure of 𝐴𝐷.


Find the measure of the minor arc 𝐶𝐷, given that the measure of the minor arc 𝐴𝐷=168 and the measure of the major arc 𝐵𝐶=256.


𝑀 is a circle, where 𝐴𝐵 is a chord and 𝐶𝐷 is a tangent. If 𝐴𝐵𝐶𝐷 and the measure of 𝐴𝐵=72, find the measure of 𝐵𝐶.


In the following figure, 𝑀 is a circle , 𝐴𝐵 and 𝐶𝐷 are two chords of the circle, and 𝐸𝐹 is a tangent to the circle at 𝐸. If 𝐴𝐵𝐶𝐷𝐸𝐹, the measure of 𝐴𝐶=30, and the measure of 𝐷𝐸=74, find the measure of 𝐴𝐵.


In the following figure, 𝐴𝐵𝐶 is an equilateral triangle inscribed in a circle. 𝐴𝐵 and 𝐷𝐸 are two chords of the circle, and 𝐹𝐺 is a tangent to the circle at 𝐹. If 𝐷𝐸𝐴𝐵𝐹𝐺 and the measure of 𝐶𝐷=79, find the measure of 𝐸𝐵.

Find the measure of 𝐷𝐹.


In the following figure, 𝐴𝐵 and 𝐸𝐹 are two equal chords. 𝐵𝐶 and 𝐹𝐸 are two parallel chords. If the measure of 𝐴𝐶=120, find the measure of 𝐶𝐸.

This lesson includes 20 additional questions and 234 additional question variations for subscribers.

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