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 𝐸𝐢=4, 𝐸𝐷=15, and 𝐸𝐡=6, find the length of 𝐸𝐴.


If 𝐸𝐴𝐸𝐡=87, 𝐸𝐢=7cm, and 𝐸𝐷=8cm, find the lengths of 𝐸𝐡 and 𝐸𝐴.

  • A𝐸𝐡=7cm, 𝐸𝐴=8cm
  • B𝐸𝐡=6.12cm, 𝐸𝐴=9.14cm
  • C𝐸𝐡=8cm, 𝐸𝐴=7cm
  • D𝐸𝐡=9.14cm, 𝐸𝐴=6.12cm


If 𝐸𝐢=10cm, 𝐸𝐷=6cm, 𝐸𝐡=5cm, find the length of 𝐸𝐴.


Given that the points 𝐴, 𝐡, 𝐢, and 𝐷 lie on a circle, find the length of 𝐡𝐴.


A circle has center 𝑀 and radius 13 cm. A line passes through the points 𝐡, 𝐢, and 𝐷 where 𝐢 and 𝐷 are on the circle, 𝐡 is 25 cm from the point 𝑀, and 𝐢𝐡=𝐢𝐷. Calculate the length of 𝐢𝐷 and the perpendicular distance π‘₯ between the line and the point 𝑀. Round your answers to 2 decimal places.

  • A𝐢𝐷=2.45cm, π‘₯=12.94cm
  • B𝐢𝐷=15.10cm, π‘₯=10.58cm
  • C𝐢𝐷=114.00cm, π‘₯=113.26cm
  • D𝐢𝐷=7.55cm, π‘₯=13.00cm


In the figure shown, the circle has a radius of 12 cm, 𝐴𝐡=12cm, and 𝐴𝐢=35cm. Determine the distance from 𝐡𝐢 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


Find length 𝐡𝐢 to the nearest integer.


Given that 𝐴𝐡 is tangent to the circle and that 𝐷 and 𝐢 lie on the circle, determine the value of π‘₯ to the nearest tenth.


Given that 𝐸𝐴=5.2cm, 𝐸𝐢=6cm, 𝐸𝐡=7.5cm, and 𝐸𝐷=6.5cm, do the points 𝐴, 𝐡, 𝐢, and 𝐷 lie on a circle?

  • AYes
  • BNo


Points 𝐴, 𝐸, 𝐡 and 𝐷, 𝐸, 𝐢 are collinear. Suppose that 𝐸𝐴=7.3, 𝐸𝐢=5.2, 𝐸𝐡=5.8, and 𝐸𝐷=7.6. Do points 𝐴, 𝐡, 𝐢, and 𝐷 lie on a circle?

  • ANo
  • BYes

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