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Intermediate Geometry : Chords

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Example Questions

Example Question #141 : Intermediate Geometry

If a chord is units away from the center of a circle, and the radius is , what is the length of that chord?

Possible Answers:

4.351

17.456

8.718

Correct answer:

8.718

Explanation:

Draw a segment perpendicular to the chord from the center, and this line will bisect the chord. Setting up the Pythagorean Theorem with the radius as the hypotenuse and the distance as one of the legs, we solve for the other leg.

$10^2-9^2=19 \rightarrow \sqrt{19}=4.3589$

Since this leg is half of the chord, the total chord length is 2 times that, or 8.718.

2(4.3589)=8.718

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Example Question #11 : Chords

If a chord is units away from the center of a circle, and the radius is , what is the length of that chord?

Possible Answers:

3.464

6.928

13.856

Correct answer:

6.928

Explanation:

$4^2-2^2=12 \rightarrow \sqrt{12}=3.4641$

Since this leg is half of the chord, the total chord length is 2 times that, or 6.928.

2(3.4641)=6.928

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Example Question #142 : Plane Geometry

If a chord is units away from the center of a circle, and the radius is , what is the length of that chord?

Possible Answers:

26.832

13.416

6.708

Correct answer:

13.416

Explanation:

$9^2-6^2=45 \rightarrow \sqrt{45}=6.7082$

Since this leg is half of the chord, the total chord length is 2 times that, or 13.416.

2(6.7082)=13.416

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Example Question #144 : Plane Geometry

Find the measure of AB in the below circle.

Chords

Possible Answers:

Correct answer:

Explanation:

When two chords intersect inside of a circle, one can find the length of the chord for this particular problem by solving the below equation.

(AQ)(BQ)=(CQ)(DQ)

Substitute the given information from the diagram.

Chords

$\\(x)(40)=(25)(16) \\40x=400 \\x=10$

Now we add 10 to 40 to find the total length from A to B.

AB=50.

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Example Question #145 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

9.81

13.94

14.42

15.22

Correct answer:

14.42

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{14^2-12^2}=\sqrt{52}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{52}=14.42$

Make sure to round to places after the decimal.

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Example Question #146 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

5.20

15.55

10.39

9.29

Correct answer:

10.39

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{6^2-3^2}=\sqrt{27}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{27}=10.39$

Make sure to round to places after the decimal.

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Example Question #147 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

6.69

9.08

8.25

4.12

Correct answer:

8.25

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{9^2-8^2}=\sqrt{17}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{17}=8.25$

Make sure to round to places after the decimal.

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Example Question #148 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

4.35

5.66

12.10

9.80

Correct answer:

9.80

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{7^2-5^2}=\sqrt{24}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{24}=9.80$

Make sure to round to places after the decimal.

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Example Question #151 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

16.21

15.10

9.03

7.55

Correct answer:

15.10

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{11^2-8^2}=\sqrt{57}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{57}=15.10$

Make sure to round to places after the decimal.

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Example Question #152 : Plane Geometry

Find the length of the chord in the figure below.

Possible Answers:

3.31

6.63

7.62

5.19

Correct answer:

6.63

Explanation:

When a chord is intercepted by a perpendicular line segment originating at the center of the circle, the chord is bisected, or cut in half.

Thus, we can use the Pythagorean Theorem to find the half of the chord that acts as the other leg of the right triangle that is created.

$\text{Half Chord}=\sqrt{\text{radius}^2-\text{leg}^2}$

$\text{Half Chord}=\sqrt{6^2-5^2}=\sqrt{11}$

Multiply this by to find the length of the entire chord.

$\text{Length of chord}=2\sqrt{11}=6.63$

Make sure to round to places after the decimal.

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Intermediate Geometry : Chords

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #141 : Intermediate Geometry

Example Question #11 : Chords

Example Question #142 : Plane Geometry

Example Question #144 : Plane Geometry

Example Question #145 : Plane Geometry

Example Question #146 : Plane Geometry

Example Question #147 : Plane Geometry

Example Question #148 : Plane Geometry

Example Question #151 : Plane Geometry

Example Question #152 : Plane Geometry

All Intermediate Geometry Resources

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