Worksheet: Properties of Circles

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In this worksheet, we will practice identifying and using parts of a circle, such as the radius, chord, and diameter, to solve problems.

Q1:

Find the length of 𝑀 𝑁 .

Q2:

Identify all the radii in the following circle:

  • A 𝐵 𝐸 , 𝐹 𝐶
  • B 𝐹 𝐷
  • C 𝑁 𝐵 , 𝑁 𝐶 , 𝑁 𝐸 , 𝑁 𝐹

Q3:

Given that 𝐴 𝐵 = 4 2 c m and 𝐸 𝐶 = 1 0 c m in the two concentric circles shown below, find the length of 𝐴 𝐶 .

Q4:

Suppose 𝐴 𝐵 = 1 3 2 c m , 𝑀 𝐷 = 4 4 . 5 c m , and 𝑀 𝐸 = 2 6 . 7 c m . What is the length of 𝐵 𝐷 ?

Q5:

Are all the radii of a circle equal in length?

  • Ayes
  • Bno

Q6:

Is the diameter the longest chord in a circle?

  • Ayes
  • Bno

Q7:

The length of the radius of a circle is the length of its diameter.

  • A half
  • B equal to
  • C twice

Q8:

What is the name of a chord that passes through the center of a circle?

  • AThe center
  • BA radius
  • CA diameter

Q9:

Which of the following correctly defines a circle?

  • AA circle is the set of points in a plane that are different distances away from the center.
  • BA circle is the set of points in a plane that are the same distance from the a given point called the center.
  • CA circle is the set of points in a plane that does not have any lines of symmetry.
  • DA circle is the set of points in a plane with a single curved side.
  • EA circle is the set of points in a plane with a limited number of sides.

Q10:

In the given figure, which of the following would represent the chord passing through 𝐵 and 𝐶 ?

  • A 𝐵 𝐶
  • B ⃖ ⃗ 𝐵 𝐶
  • C 𝐵 𝐶
  • D 𝐶 𝐵
  • E 𝐵 𝐶

Q11:

Identify the radii of the circle.

  • A 𝐸 𝐻 , 𝐸 𝐹 , 𝐹 𝐺 , 𝐺 𝐻
  • B 𝐸 𝐺 , 𝑀 𝐻 , 𝑀 𝐺 , 𝐸 𝐹
  • C 𝑀 𝐸 , 𝑀 𝐹 , 𝐸 𝐹 , 𝑀 𝐻
  • D 𝑀 𝐸 , 𝑀 𝐹 , 𝑀 𝐺 , 𝑀 𝐻

Q12:

Identify the diameter of this circle.

  • A 𝑀 𝐵
  • B 𝐴 𝐵
  • C 𝐴 𝐶
  • D 𝑀 𝐴

Q13:

Given that 𝐴 𝐵 = 1 5 c m , find the radius to the circle 𝑀 .

Q14:

If the length of diameter 𝐴 𝐵 of circle 𝑀 is 158 cm, find the radius of the circle.

Q15:

Determine the diameter of the circle 𝑀 , given that its radius 𝐴 𝑀 = 4 9 c m .

Q16:

What is the radius of a circle whose diameter is 18?

Q17:

What is the diameter of a circle whose radius is 3?

Q18:

If the diameters of circles 𝑀 and 𝑁 are 2 cm and 6 cm, respectively, determine the length of 𝑀 𝑁 .

Q19:

Circles 𝑀 and 𝑁 are of radii 11 and 18 and touch internally. Determine 𝑀 𝑁 .

  • A15
  • B7
  • C29
  • D18
  • E11

Q20:

What is the name for any line segment in a circle whose endpoints intersect the circle?

  • A chord
  • B a quarter of
  • C twice

Q21:

If the length of the longest chord in a circle is 310 cm, what is its radius?

Q22:

Chords 𝐴 𝐵 and 𝐶 𝐷 meet at 𝐸 . If the lengths 𝐴 𝐸 , 𝐵 𝐸 , and 𝐶 𝐷 are 5, 6.4, and 12 respectively, what are the possible values for 𝐸 𝐶 ?

  • A8 or 4
  • B8 or 5
  • C5 or 6.4
  • D4 or 6.4

Q23:

Determine the chord(s) of the circle shown below.

  • A 𝑁 𝐸 , 𝑁 𝐹 , 𝑁 𝐺 , 𝑁 𝐾 , 𝑁 𝐿
  • B 𝐿 𝐺 , 𝐹 𝐾
  • C 𝐸 𝐹 , 𝐹 𝐺 , 𝐿 𝐻 , 𝐿 𝐺 , 𝐹 𝐾

Q24:

In the figure, 𝑀 𝐴 = 3 4 c m . Determine the length of 𝐶 𝐸 .

Q25:

What is the longest segment with endpoints on a circle of radius 66.9 cm?

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