### All Intermediate Geometry Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 #1 : 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:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

Since this leg is half of the chord, the total chord length is 2 times that, or 9.592.

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