3. Given that point $P$ moves on the line $y=x+2$, points $A(2,2)$ and $B(6,6)$ satisfy that $\angle APB$ reaches its maximum value. Then the coordinates of point $P$ are ( ).
(A) $(0,2)$
(B) $(1,3)$
(C) $(2,4)$
(D) $(3,5)$
3.D.

From the image, we can see that the point of tangency $P$ between the circle passing through $A$ and $B$ and the line is the point $P$, so the coordinates of point $P$ are $(3,5)$.