Circle Properties - Chords?

Question

a)How many chords can you draw anywhere on a circle that are the same length as a given chord?

b)Make a statement about the realitive distance of each chord from the center of the circle

c)Make a statement about the position of beams of the same length in the ceiling of a domed arena.

Answer 1

a. An infinite number of such cords are possible.

b. If you draw a line from the center of the circle that is perpendicular to each chord from a above, then all those lines would be of the same length. Therefore, all chords of the same size will be equidistant from the center of the circle.

c. Based on b, all the beams would be of the same length since they are equidistant from the center of the dome.

Answer 2

An infinite number.

Are we talking about the chords mentioned in A? They are all the same distance from the center of the circle. In general, the maximum distance from a chord to the center of the circle is the length of the radius.

Beams of the same length are going to be equidistant from the focus of the circle which forms the dome.