Question

find the value of x.

Explanation:

Step1: Apply the perpendicular from the center to a chord property

In a circle, if a perpendicular is drawn from the center to a chord, it bisects the chord. So, the length of the chord with the segment \(9\) is \(2\times9 = 18\).

Step2: Use the property of chords equidistant from the center

Chords that are equidistant from the center of a circle are equal in length. The distance from the center \(O\) to both chords is \(7\). Since the two chords are equidistant from the center, they are equal in length. If one - half of the first chord (the one with the segment \(9\) when bisected) is \(9\), and the other chord is bisected into segments \(x\).

Answer:

\(x = 9\)