Question

question 34 of 44
what is the length of (overline{ac})?
diagram: circle with center o, chord (ac), (m) is midpoint, (om perp ac), (am = 12)
a. 48
b. 12
c. 6
d. 24

Explanation:

Step1: Recall the perpendicular chord bisector theorem

A line from the center of a circle perpendicular to a chord bisects the chord. So, \( AM = MC \).

Step2: Calculate the length of \( \overline{AC} \)

Given \( AM = 12 \), then \( AC = AM + MC \). Since \( AM = MC \), \( AC = 2\times AM \).
Substitute \( AM = 12 \) into the formula: \( AC = 2\times12 = 24 \).

Answer:

D. 24