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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.

Q1:

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.

Q2:

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

  • A
  • B
  • C
  • D
  • E

Q3:

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

Q4:

Find 𝑚𝐵𝐸 where 𝑀 is the center of the circle.

Q5:

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

Q6:

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.

Q7:

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.

Q8:

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.

Q9:

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.

Q10:

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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