The Parts of a Circle - Examples, Exercises and Solutions

Central angle in a circle

We are here to define what a central angle in a circle is and give you tips to remember its definition and properties in the best and most logical way.
Before talking about the central angle in a circle, let's take a moment to look at its name - a central angle.

Through its name, we can recognize that it has some connection with the center of the circle.
Great, now let's move on to the definition of a central angle and it will make much more sense to us.

Image A1 - A central angle in a circle

What is a central angle in a circle?

A central angle in a circle is an angle whose vertex is the center of the circle and its ends are the radii of the circle
Therefore, its ends are on the top part of the circle.
If we connect all the central angles in the same complete circle - we will obtain 360° 360° .

Practice The Parts of a Circle

Exercise #1

In which of the circles is the segment drawn the radius?

Video Solution

Answer

Exercise #2

In which of the circles is the point marked in the circle and not on the circumference?

Video Solution

Answer

Exercise #3

Calculate the length of the arc marked in red given that the circumference is 12.

240

Video Solution

Answer

8

Exercise #4

Calculate the length of the arc marked in red given that the circumference is 12.

60°60°60°

Video Solution

Answer

2

Exercise #5

Calculate the length of the arc marked in red given that the circumference is 6.

50

Video Solution

Answer

56 \frac{5}{6}

Exercise #1

Calculate the area of the section painted red given that the area of the circle is 12.

240

Video Solution

Answer

8

Exercise #2

Calculate the length of the arc marked in red given that the circumference is 36.

20

Video Solution

Answer

2

Exercise #3

How many times longer is the radius of the red circle than the radius of the blue circle?

220

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Answer

5

Exercise #4

How many times longer is the radius of the red circle, which has a diameter of 24, than the radius of the blue circle, which has a diameter of 12?

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Answer

2

Exercise #5

How many times longer is the radius of the red circle than the radius of the blue circle?

168

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Answer

2 2

Exercise #1

Calculate the length of the arc marked in red given that the circumference is equal to 24.

150°150°150°

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Answer

10 10

Exercise #2

Calculate the length of the arc marked in red given that the circumference is 18.

260°260°260°

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Answer

13

Exercise #3

How many times longer is the radius of the red circle (14 cm) than the radius of the blue circle, which has a diameter of 7?

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Answer

4

Exercise #4

How many times longer is the radius of the red circle than the radius of the blue circle?

210

Video Solution

Answer

212 2\frac{1}{2}

Exercise #5

Calculate the area of the section shaded in red given that the area of the circle is 36.

20°20°20°

Video Solution

Answer

2 2

Topics learned in later sections

  1. Circle
  2. Distance from a chord to the center of a circle
  3. Chords of a Circle
  4. Arcs in a Circle
  5. Perpendicular to a chord from the center of a circle
  6. Inscribed angle in a circle
  7. Tangent to a circle
  8. Area of a circle
  9. The Circumference of a Circle
  10. How is the radius calculated using its circumference?