Question

question 9 of 10
if the blue radius below is perpendicular to the green chord and the segment
\\( \overline { a b } \\) is 6.5 units long, what is the length of the chord?
a. 3.25 units
b. 26 units
c. 6.5 units
d. 13 units

Explanation:

Step1: Apply the perpendicular - radius theorem

The perpendicular - radius theorem states that if a radius of a circle is perpendicular to a chord, then it bisects the chord. So, if the radius is perpendicular to the chord \(AC\), then \(AB = BC\).

Step2: Calculate the length of the chord

Given \(AB=6.5\) units. Since \(AC = AB + BC\) and \(AB = BC\) (by the perpendicular - radius theorem), then \(AC=2\times AB\).
Substitute \(AB = 6.5\) into the formula: \(AC=2\times6.5\)

Answer:

\(13\) units, so the answer is D.