Final answer:
The circumference of the circle with the given center and point is approximately (c) 38 units, calculated using the formula C = 2πr with the radius found from the distance between the given points.
Step-by-step explanation:
The student is tasked with identifying the approximate circumference of a circle with a given center and a point on its circumference. To solve this, we must first determine the radius of the circle. The distance between the center (8,6) and the point (8,12) is 6 units, which is the radius (r) of the circle. The formula for circumference (C) is given by C = 2πr. Plugging in our value of r:
C = 2π(6) ≈ 2(3.14159)(6) ≈ 37.6991
The approximate circumference of the circle is therefore c)38 units, which is the closest approximation to the actual calculated value.