Lesson Worksheet: Special Segments in a Circle Mathematics

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:

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

Q2:

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

Q3:

In the following figure, find the value of 𝑥.

Q4:

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

Q5:

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

Q6:

What is the radius of circle 𝑀?

Q7:

In the following figure, find the value of 𝑥.

Q8:

Given that 𝐸𝐶=12, 𝐸𝐷=11, and 𝐸𝐵=12, find the length of 𝐸𝐴.

Q9:

If 𝐸𝐴𝐸𝐵=92, 𝐸𝐶=3cm, and 𝐸𝐷=6cm, find the lengths of 𝐸𝐵 and 𝐸𝐴.

  • A𝐸𝐵=2cm, 𝐸𝐴=9cm
  • B𝐸𝐵=1cm, 𝐸𝐴=18cm
  • C𝐸𝐵=4.5cm, 𝐸𝐴=13.5cm
  • D𝐸𝐵=9cm, 𝐸𝐴=2cm
  • E𝐸𝐵=18cm, 𝐸𝐴=1cm

Q10:

Given that 𝐸𝐴=7.5cm, 𝐸𝐶=5.6cm, 𝐸𝐵=7.9cm, and 𝐸𝐷=6cm, do the points 𝐴, 𝐵, 𝐶, and 𝐷 lie on a circle?

  • ANo
  • BYes

Q11:

Points 𝐴, 𝐸, 𝐵 and 𝐷, 𝐸, 𝐶 are collinear. Suppose that 𝐸𝐴=7.4, 𝐸𝐶=5.4, 𝐸𝐵=6, and 𝐸𝐷=7. Do points 𝐴, 𝐵, 𝐶, and 𝐷 lie on a circle?

  • ANo
  • BYes

Q12:

𝐴𝐵 and 𝐴𝐶 are two chords of a circle of center 𝑀 and radius 26. Suppose that 𝑀𝐾 is perpendicular to both 𝐴𝐵 and 𝐴𝐶 and contains a point 𝑁 with 𝑀𝑁=82.5. Find the lengths of 𝑁𝐵 and 𝑁𝐶.

  • A𝑁𝐵=86.5, 𝑁𝐶=86.5
  • B𝑁𝐵=26, 𝑁𝐶=86.5
  • C𝑁𝐵=26, 𝑁𝐶=82.5
  • D𝑁𝐵=86.5, 𝑁𝐶=82.5

Q13:

If 𝐸𝐴𝐸𝐵=53, 𝐸𝐶=12cm, and 𝐸𝐷=5cm, find the lengths of 𝐸𝐵 and 𝐵𝐴.

  • A𝐸𝐵=10cm, 𝐵𝐴=6cm
  • B𝐸𝐵=6cm, 𝐵𝐴=10cm
  • C𝐸𝐵=24cm, 𝐵𝐴=20cm
  • D𝐸𝐵=6cm, 𝐵𝐴=4cm
  • E𝐸𝐵=4cm, 𝐵𝐴=6cm

Q14:

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

Q15:

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

Q16:

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

Q17:

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

Q18:

Are the points 𝐴, 𝐵, 𝐶, and 𝐷 lying on a circle?

  • ANo
  • BYes

Q19:

Given that 𝐸𝐴=11𝑥, 𝐸𝐵=21𝑥, 𝐸𝐶=22, and 𝐸𝐷=42, find the value of 𝑥.

  • A𝑥=2
  • B𝑥=0.55
  • C𝑥=46.2
  • D𝑥=1.05

Q20:

Given that the circle of center 𝑀 shown below has a radius of 25 cm, 𝐴𝐵=36cm, and 𝐶𝐷=48cm, find the length of 𝑀𝑂.

  • A14 cm
  • B30 cm
  • C514 cm
  • D25 cm

Q21:

𝐴𝐵 and 𝐶𝐷 are two chords of a circle intersecting at 𝐻. Find 𝐻𝐷, where 𝐴𝐻=10, 𝐻𝐵=8, and 𝐶𝐻=16.

  • A2
  • B20
  • C5
  • D12.8
  • E5.6

Q22:

𝐴𝐵 and 𝐶𝐷 are two intersecting line segments at 𝐻 inside a circle, where 𝐴𝐻=4, 𝐻𝐵=6, 𝐷𝐻=3, and 𝐻𝐶=8. Are 𝐴𝐵 and 𝐶𝐷 chords?

  • AYes
  • BNo

Q23:

In the given figure, 𝐴𝐵=5cm, 𝐶𝐷=9cm, and 𝐷𝐸=3cm. Find the length of 𝐵𝐸.

Q24:

Find the value of 𝑥.

Q25:

Consider a triangle 𝐴𝐷𝐸 where 𝐸𝐷=41. The point 𝐶 satisfies 𝐶𝐸𝐷, 𝐶𝐸𝐷, and 𝐶𝐷=45. 𝐸𝐴 is a tangent to the circle that passes through 𝐴, 𝐷, and 𝐶. Find the length of 𝐸𝐴 to the nearest hundredth.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.