Question

question 1 of 10
what is the length of chord \\( \overline { c d } \\) in \\( \odot o \\) below?
a. 8.31 units
b. 16.04 units
c. 8.02 units
d. 4.01 units

Explanation:

Step1: Recall the chord - distance theorem

In a circle, if two chords are equidistant from the center, then the chords are congruent. Here, chord \(AB\) and chord \(CD\) are equidistant from the center \(O\) (both have a perpendicular distance from the center, and the radii \(OA = OC\)).

Step2: Use the property of congruent chords

Since chords \(AB\) and \(CD\) are congruent (by the chord - distance theorem in a circle: if \(d_1=d_2\) (where \(d\) is the perpendicular distance from the center to the chord) and \(r_1 = r_2\) (radii of the same circle), then the chords are congruent), and the length of chord \(AB = 8.02\) units.

Answer:

B. 16.04 units