How can we prove that A', B', and C' are collinear in triangle ABC?

[SonyDvDPro]

1 ) Let $$P$$ be an arbitary point in the plane of triangle $$\vartriangle ABC$$ , let $$A'$$ be a point on $$BC$$ such that $$A'B \bot PA$$
, Define $$B' , C'$$ in the same way,P rove that $$A' , B' ,C'$$ are collinear.

 

[dodo]

I'm not sure the statement of the problem is correct; if A' is a point on segment BC, then A'B is a subsegment of BC, and the choice of A' does not affect at all the (possible or not) parallel condition with respect to PA, since all P, A, B and C are fixed beforehand.