A parallelogram ABCD with its diagonals meeting at the point O is shown in the diagram . AB is extendedto P such that BP=AB . THe line that passes through D and is parallel to AC meets PC produced at point R and angle CRD =90 .

(1) SHow that the triangles ABD and BPC are congruent .

I managed to prove this .

(2) Show that ABCD is a rhombus .

(3) CR:PC

Not sure bout (2) and (3)