To find the length of \( KI \) in the context of a circle, we need to recognize that if \( G \) is the center of the circle and \( H, I, J, K \) are points on the circumference, then all the segments from the center \( G \) to these points (i.e., \( GH, GI, GJ, GK \)) are equal because they are all radii of the circle.
Given that \( GH = 13 \) inches, we know that the radius of the circle is 13 inches. Consequently:
- \( GI = 13 \)
- \( GJ = 13 \)
- \( GK = 13 \)
To find \( KI \), we can use the central angles formed by these points on the circumference. Since points \( H \), \( I \), \( J \), and \( K \) are uniformly placed along the circumference, \( KI \) will be a chord of the circle. However, we don't have information about the specific arrangement of the points \( H, I, J, K \) on the circle, such as the angles between the radii connecting these points.
To calculate \( KI \), we need additional quantitative information about the angles or relative positions of points \( H, I, J, K \). Without that information, we cannot determine the exact length of \( KI \). The length of a chord in a circle depends on the radius and the angle subtended at the center by the chord.
In summary, without specific angles or additional context provided in the image, we cannot definitively calculate \( KI \). If they are directly across from each other, it would be equal to the diameter, which is \( 26 \) inches (double the radius), but additional context is critical for accuracy.