Distance from a chord to the center of a circle - Examples, Exercises and Solutions

The distance from the chord to the center of the circle is defined as the length of the perpendicular from the center of the circle to the chord.
Theorems on the distance from the center of the circle:

  1. Chords that are equal to each other are equidistant from the center of the circle.
  2. If in a circle, the distance of a chord from the center of the circle is less than the distance of another chord from the center of the circle, we can determine that the chord with the lesser distance is longer than the other chord.
A1 - The distance from the chord to the center of the circle

All theorems can also exist in reverse.

Practice Distance from a chord to the center 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?

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Answer

Exercise #3

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

240

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Answer

8

Exercise #4

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

60°60°60°

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Answer

2

Exercise #5

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

50

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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

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Answer

8

Exercise #2

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

20

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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°

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Answer

2 2

Topics learned in later sections

  1. Circle
  2. Chords of a Circle
  3. Central Angle in 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?