To determine the length of segment \( KI \) in the circle based on the information provided, we can use the properties of circles. Given that \( G \) is the center of the circle and \( H \), \( I \), \( J \), and \( K \) are points on the circumference, we know that all radii of the circle are equal.
Since \( GH = 13 \) inches, the radius of the circle is \( 13 \) inches. As a result, \( GJ = GK = GI = GH = 13 \) inches.
To find \( KI \), we can apply the fact that \( KI \) is a chord in the circle. However, without specific additional information about the location of points \( K \) and \( I \) relative to point \( G \) or any angles, we cannot provide a definitive length for \( KI \) just with the radius length.
In the case where \( K \) and \( I \) do not form a special case (like being diametrically opposite) or if no other data is given, we cannot calculate the exact length of \( KI \).
If \( KI \) is indeed a segment (chord) within the circle, potential values could depend on the angle subtended at \( G \) or other lengths or angles that have not been provided.
If you have more specific relationships or coordinates for points \( K \) and \( I \), please provide that for a more accurate calculation. Otherwise, based on your current question, the answer cannot be determined precisely.