A circle includes  of angle measure, so a sector of measure  is  of the circle. Set  - the sector is 

of the circle. The statement is false.

 is the center of the circle, so  is a central angle. , so its intercepted arc  also has this measure.

 is an inscribed angle which intercepts , so

Substitute:

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.

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.

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.

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.

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.

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.

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.

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.