KöMaL 2008 B4110

The hexagon ABCDEF and the triangle PQR lie in the same plane. The quadrilaterals ABRQ , CDPR , EFQP are all rectangles. $a$) Prove that the perpendicular bisectors of the sides $BC$, $DE$, $FA$ are concurrent. $b$) Show that there exists a triangle $P$'$Q$'$R$', too, for which the quadrilaterals BCR '$Q$', DEP '$R$', FAQ '$P$' are rectangles.