# Intermediate Geometry : How to find the length of a chord

## Example Questions

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### Example Question #1 : How To Find The Length Of A Chord

The radius of  is  feet and .  Find the length of chord .

Explanation:

We begin by drawing in three radii:  one to , one to , and one perpendicular to  with endpoint  on our circle.

We must also recall that our central angle  has a measure equal to its intercepted arc.  Therefore, .  Our perpendicular radius actually divides  into two congruent triangles.  Therefore, it also bisects our central angle, meaning that

Therefore, each of these triangles is a 30-60-90 triangle, meaning that each half of our chord is simply half the length of the hypotenuse (our radius which is 6).  Therefore, each half is 3, and the entire chord is 6 feet.

### Example Question #2 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 9.798.

### Example Question #3 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 16.

### Example Question #4 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 7.937.

### Example Question #5 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 3.606.

### Example Question #6 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 6.

### Example Question #7 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 13.266.

### Example Question #8 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 4.472.

### Example Question #9 : How To Find The Length Of A Chord

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

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.

Since this leg is half of the chord, the total chord length is 2 times that, or 7.746.

### Example Question #10 : How To Find The Length Of A Chord

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