3. The number of lines that are tangent to the circle $(x-2)^{2}+y^{2}=1$ and have equal intercepts on both coordinate axes is ( ).
(A) 2
(B) 3
(C) 4
(D) 6
3. C.

From the combination of numerical and graphical analysis, we know that the lines tangent to the circle and having equal intercepts on the two coordinate axes are divided into two categories:
(1) There are 2 lines passing through the origin that satisfy the condition;
(2) There are also 2 lines with a slope of -1 that satisfy the condition.
In total, there are 4 lines.