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.

please help(Crying)

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- July 18th 2010, 11:44 PMearthboya triangle geometry...
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.

please help(Crying) - July 19th 2010, 12:28 AMsimplependulum
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 .