If the coordinates of circle Z refer to its centre, then (x-5)2+(y-2)2=a2, where a is the unknown radius. [However, we know (1,7) is a tangent so it must lie on the circle, therefore:
(1-5)2+(7-2)2=16+25=41=a2, making the equation of Z (x-5)2+(y-2)2=41. This information is not needed to find the slope because the derivative of the constant a2 is zero.]
Differentiate (x-5)2+(y-2)2=a2 to get the slope dy/dx:
2(x-5)+2(y-2)dy/dx=0, dy/dx=(5-x)/(y-2).
At (1,7), dy/dx=(5-1)/(7-2)=⅘. The slope of CD=⅘.