Let triangle MNP right angled at M , altitude MH . a) Prove that AHNM is similar to AMNP.
b) Prove the relation MH? = NH. PH.
c) Take an arbitrary point E on edge MP ( E is different from M ; P ), draw a point F on edge MN such that FHE = 90° , EF intersects MH at point I. Prove that ANPH is similar to AMEH and FMI = FEH .
d ) Determine the position of point E on MP so that the area AHEF reaches the minimum value .