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

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

Q1:

Given that 𝐸𝐶=4, 𝐸𝐷=15, and 𝐸𝐵=6, find the length of 𝐸𝐴.

Q2:

If 𝐸𝐴𝐸𝐵=87, 𝐸𝐶=7cm, and 𝐸𝐷=8cm, find the lengths of 𝐸𝐵 and 𝐸𝐴.

  • A𝐸𝐵=7cm, 𝐸𝐴=8cm
  • B𝐸𝐵=6.12cm, 𝐸𝐴=9.14cm
  • C𝐸𝐵=8cm, 𝐸𝐴=7cm
  • D𝐸𝐵=9.14cm, 𝐸𝐴=6.12cm

Q3:

If 𝐸𝐶=10cm, 𝐸𝐷=6cm, 𝐸𝐵=5cm, find the length of 𝐸𝐴.

Q4:

Given that the points 𝐴, 𝐵, 𝐶, and 𝐷 lie on a circle, find the length of 𝐵𝐴.

Q5:

A circle has center 𝑀 and radius 13 cm. A line passes through the points 𝐵, 𝐶, and 𝐷 where 𝐶 and 𝐷 are on the circle, 𝐵 is 25 cm from the point 𝑀, and 𝐶𝐵=𝐶𝐷. Calculate the length of 𝐶𝐷 and the perpendicular distance 𝑥 between the line and the point 𝑀. Round your answers to 2 decimal places.

  • A𝐶𝐷=2.45cm, 𝑥=12.94cm
  • B𝐶𝐷=15.10cm, 𝑥=10.58cm
  • C𝐶𝐷=114.00cm, 𝑥=113.26cm
  • D𝐶𝐷=7.55cm, 𝑥=13.00cm

Q6:

In the figure shown, the circle has a radius of 12 cm, 𝐴𝐵=12cm, and 𝐴𝐶=35cm. Determine the distance from 𝐵𝐶 to the center of the circle, 𝑀, and the length of 𝐴𝐷, 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

Q7:

Find length 𝐵𝐶 to the nearest integer.

Q8:

Given that 𝐴𝐵 is tangent to the circle and that 𝐷 and 𝐶 lie on the circle, determine the value of 𝑥 to the nearest tenth.

Q9:

Given that 𝐸𝐴=5.2cm, 𝐸𝐶=6cm, 𝐸𝐵=7.5cm, and 𝐸𝐷=6.5cm, do the points 𝐴, 𝐵, 𝐶, and 𝐷 lie on a circle?

  • AYes
  • BNo

Q10:

Points 𝐴, 𝐸, 𝐵 and 𝐷, 𝐸, 𝐶 are collinear. Suppose that 𝐸𝐴=7.3, 𝐸𝐶=5.2, 𝐸𝐵=5.8, and 𝐸𝐷=7.6. Do points 𝐴, 𝐵, 𝐶, and 𝐷 lie on a circle?

  • ANo
  • BYes

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