To find the distance from the center of the circle x^2 + y^2 = 2x to the straight line passing through the points of intersection of the two circles x^2 + y^2 - 5x - 8y + 1 = 0 and x^2 + y^2 - 3x + 7y - 25 = 0, we need to follow these steps:

1. Find the center and radius of the first circle:
The given equation of the first circle is x^2 + y^2 = 2x. We can rewrite it as (x-1)^2 + y^2 = 1. This represents a circle with center (1, 0) and radius 1.

2. Find the points of intersection of the two circles:
By solving the two given equations simultaneously, we can find the points of intersection. By subtracting the second equation from the first, we get -2x - 15y + 26 = 0. Solving this equation along with x^2 + y^2 - 5x - 8y + 1 = 0 will give us two values of x. Substituting these values back into either equation will give us the corresponding y values.

3. Find the equation of the line passing through the points of intersection:
Using the slope-intercept form, we can find the equation of the line passing through the points of intersection. The slope can be found by dividing the difference in y-coordinates by the difference in x-coordinates. Then, using one of the points and the slope, we can find the y-intercept.

4. Find the perpendicular distance from the center to the line:
The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by the formula:
Distance = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line passing through the points of intersection is known, and the center of the first circle is (1, 0). By substituting these values into the formula, we can find the perpendicular distance.

5. Calculate the distance:
By substituting the values into the formula, the perpendicular distance from the center of the circle to the line passing through the points of intersection can be calculated.

The correct answer is option B, which represents a distance of 2.