Lesson Worksheet: Special Segments in a Circle Mathematics • 11th Grade

In this worksheet, we will practice using the theorems of intersecting chords, secants, or tangents and secants to find missing lengths in a circle.


Given that ๐ธ๐ถ=4, ๐ธ๐ท=15, and ๐ธ๐ต=6, find the length of ๐ธ๐ด.


If ๐ธ๐ด๐ธ๐ต=87, ๐ธ๐ถ=7cm, and ๐ธ๐ท=8cm, find the lengths of ๐ธ๐ต and ๐ธ๐ด.

  • A๐ธ๐ต=7cm, ๐ธ๐ด=8cm
  • B๐ธ๐ต=6.12cm, ๐ธ๐ด=9.14cm
  • C๐ธ๐ต=8cm, ๐ธ๐ด=7cm
  • D๐ธ๐ต=9.14cm, ๐ธ๐ด=6.12cm


In the following figure, find the value of ๐‘ฅ.


If ๐ธ๐ถ=10cm, ๐ธ๐ท=6cm, ๐ธ๐ต=5cm, find the length of ๐ธ๐ด.


Given that the points ๐ด, ๐ต, ๐ถ, and ๐ท lie on a circle, find the length of ๐ต๐ด.


A circle has center ๐‘€ and radius 13 cm. A line passes through the points ๐ต, ๐ถ, and ๐ท where ๐ถ and ๐ท are on the circle, ๐ต is 25 cm from the point ๐‘€, and ๐ถ๐ต=๐ถ๐ท. Calculate the length of ๐ถ๐ท and the perpendicular distance ๐‘ฅ between the line and the point ๐‘€. Round your answers to 2 decimal places.

  • A๐ถ๐ท=2.45cm, ๐‘ฅ=12.94cm
  • B๐ถ๐ท=15.10cm, ๐‘ฅ=10.58cm
  • C๐ถ๐ท=114.00cm, ๐‘ฅ=113.26cm
  • D๐ถ๐ท=7.55cm, ๐‘ฅ=13.00cm


In the figure shown, the circle has a radius of 12 cm, ๐ด๐ต=12cm, and ๐ด๐ถ=35cm. Determine the distance from ๐ต๐ถ to the center of the circle, ๐‘€, and the length of ๐ด๐ท, rounding your answers to the nearest tenth.

  • A19.6 cm, 20.2 cm
  • B3.4 cm, 26.6 cm
  • C3.4 cm, 20.5 cm
  • D11.5 cm, 20.2 cm


Find length ๐ต๐ถ to the nearest integer.


Given that ๐ด๐ต is tangent to the circle and that ๐ท and ๐ถ lie on the circle, determine the value of ๐‘ฅ to the nearest tenth.


Given that ๐ธ๐ด=5.2cm, ๐ธ๐ถ=6cm, ๐ธ๐ต=7.5cm, and ๐ธ๐ท=6.5cm, do the points ๐ด, ๐ต, ๐ถ, and ๐ท lie on a circle?

  • AYes
  • BNo

This lesson includes 31 additional questions and 286 additional question variations for subscribers.

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