let in triangle ABC,AB=AC. D is the midpoint of BC.E is the foot of the perpendicular from D to AB,and F is the midpoint of DE.
Prove that AF is perpendicular to CE.
This is a problem of USSR MO , i have solved it already .
Let be the mid-pt of , from we have .
Then consider that so
because is the mid-pt of while is the mid-pt of
We can find that is perpendicular to .
( Median perpendicular to median as sides perpendicular to sides , check it ! )
Therefore , is perpendicular to as mentioned before .