I am not sure I understand your question but I assumed that you have a circular arc. Let us know if we haven't interpreted the question correctly.
I drew a diagram, labeled the radius r an drew a line from the centre C to the midpoint of the arc.
The triangle ABC is a right triangle so, by Pythagoras theorem,
52 + (r - 2)2 = r2, or
25 + r2 - 4r + 4 = r2, or
r = 29/4 = 7.25 inches.
Thus you need pipe with a diameter of 14.5 inches.
If you need to find the length of the arc then that involves some trigonometry.
cos(BCA) = (r - 2)/r = 5.25/7.25 = 0.7241
and hence the measure of angle BCA is cos-1(0.7241) = 0.7610 radians and thus the measure of angle DCA is 2 0.7610 = 1.522 radians.
The length a of the arc is given by
a = r angle(DCA) = 7.25 1.522 = 11.42 inches o almost 11.5 inches.