Let BD be an altitude of ΔABC with D between A and C (not the midpoint).
The bisector of ∠ACB intersects BD and AB in points P
and Q respectively. The bisector of ∠CAB intersects BD
and BC in points R and S respectively. F and G are the
midpoints of PQ and RS respectively.
Prove that FG is parallel with AC if and only if ∠ABC = 90°.