Question

question 3 of 10
fill in the blank. two chords that are the same distance from the center of a circle must be _.
a. perpendicular
b. congruent
c. radii
d. parallel

Explanation:

In a circle, the length of a chord is related to its distance from the center. The formula for the length of a chord \(l = 2\sqrt{r^{2}-d^{2}}\), where \(r\) is the radius of the circle and \(d\) is the distance from the center of the circle to the chord. If two chords have the same distance \(d\) from the center (and the same radius \(r\) as they are in the same circle), then their lengths \(l\) will be equal. Congruent chords are chords that have the same length.

• Option A: Perpendicular chords do not necessarily have the same distance from the center. For example, two perpendicular chords of different lengths can exist in a circle.
• Option C: Radii are line - segments from the center to the circumference, not chords.
• Option D: Parallel chords can have different lengths (and thus different distances from the center).

Answer:

B. congruent