Given information:
- The center of the circle is (2 - 1, 7).
- The circle passes through the point (-3, 1).
- The diameter of the circle is 20 units.

Approach:
To find the values of ?, we need to determine the radius and the equation of the circle. Once we have the equation, we can easily find the values of ?.

Steps:

1. Find the radius:
- The radius of a circle is the distance from its center to any point on its circumference.
- In this case, we can use the distance formula to find the radius.
- Let's consider the center of the circle as point A (2, 7) and the point on the circumference as point B (-3, 1).
- The distance between A and B is the radius of the circle.
- Using the distance formula, the radius (r) can be calculated as follows:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
r = sqrt((-3 - 2)^2 + (1 - 7)^2)
r = sqrt((-5)^2 + (-6)^2)
r = sqrt(25 + 36)
r = sqrt(61)

2. Find the equation of the circle:
- The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
- Substituting the values, we have:
(x - 2)^2 + (y - 7)^2 = (sqrt(61))^2
(x - 2)^2 + (y - 7)^2 = 61

3. Find the values of ?:
- The symbol ? represents the perimeter of the circle.
- The perimeter of a circle is given by the formula: ? = 2πr
- Substituting the value of r (sqrt(61)) into the formula, we have:
? = 2π(sqrt(61))
- Evaluating this expression using the value of π (approximately 3.14159), we can find the value of ?.

Final Answer:
The values of ? can be found by evaluating the expression 2π(sqrt(61)).

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