Geometry

Question Analysis

The main focus is leveraging the property that chords equidistant from the center of a circle are equal in length. Given the visual indication of equal distances from the center to the chords, we'll use this property to find the value of .

 

Key Concept Explanation

In a circle, when two chords are perpendicular to lines from the center (such that the distances from the center to these chords are equal, as shown by the equal markings in the diagram), the chords have equal lengths. This is a fundamental property for solving problems related to circle chords.

 

Step - by - Step Solution

1. Observe that the two chords are equidistant from the center of the circle, as indicated by the equal - length segments from the center to the chords.

2. According to the property of chords equidistant from the center, the lengths of these chords are equal.

Since the given length of one chord (half of it is shown as 13) implies the full length of that chord is

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