Answer:
9 1/16 in
Explanation:
When chords cross, the distances from their point of intersection to the circle have the same product for each chord. For the 9-in chord, those two distances are 4.5 inches. For the diameter, the distances are 4 in and (d-4) in, where d is the diameter of the circle. Then ...
4.5^2 = 4(d -4)
d = 4.5^2/4+4 = 9 1/16 . . . . inches
The diameter is 9 1/16 inches.
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Comment on the diagram
The fact that the 9-inch chord looks very much like a diameter tells you the actual diameter won't be much different than that. These figures are not always drawn to scale, and are sometimes misleading. However, if the actual diameter were in the neighborhood of 16 inches, the perpendicular bisector shown would need to be about 1.4 inches instead of 4 inches.