4. In $\triangle A B C$, $A B=A C, \angle A=36^{\circ}$, $P$ is a point in the plane of $\triangle A B C$, and $\triangle P A B$, $\triangle P B C$, $\triangle P A C$ are all isosceles triangles. Then the number of points $P$ that satisfy this condition is ( ) .
(A) 10
(B) 8
(C) 6
(D) 4
4. B.

As shown in Figure 2, when $B P = C P$, point $P$ lies on the perpendicular bisector of $B C$, and there are 4 points that meet the requirement;

When $B C = B P$, point $P$ lies on the circle $\odot B$ with $B C$ as the radius, and there are 2 points that meet the requirement;

Similarly, when $B C = C P$, there are 2 points that meet the requirement.