43. Point E is the moving point on the broken line A-D-C (point E does not coincide with point A), and point P is the symmetrical point of point A about BE. During the movement of point E, the position of point E that makes △PCB an isosceles triangle * * has ().

(Sorry, the picture was not found)

Answer, 2

b，3

c，4

d，5

Test center: determination of isosceles triangle.

Special topic: classified discussion.

Analysis: according to the meaning of the question, combined with the figure, it is discussed in different situations: ①BP is the bottom; ②BP is an isosceles triangle with waist length.

Solution: Solution: ① When BP is the bottom, there are two positions intersecting with point E;

② When BP is an isosceles triangle with waist length, there are two positions corresponding to point E;

③ When PC is the base and B is the vertex, such an isosceles triangle does not exist.

So choose C.