Let's solve this circle arc length problem. We are given a circle with center O and a circumference of 36. We need to find the length of minor arc AC. From the diagram, we can see that angle AOC appears to be a right angle, which is 90 degrees.To find the arc length, we use the formula: arc length equals the central angle divided by 360 degrees, multiplied by the circumference. Since angle AOC is 90 degrees and the circumference is 36, we substitute these values. Arc AC equals 90 over 360, times 36. This simplifies to one-fourth times 36, which equals 9. Therefore, the length of minor arc AC is 9, and the answer is A.Let's verify our answer. A full circle has 360 degrees. The arc AC corresponds to a 90-degree angle, which is one-fourth of the full circle. Since the circumference is 36, one-fourth of 36 equals 9. This confirms that the length of minor arc AC is 9. Therefore, the correct answer is A.