1. ## difficult proof!

AD is an altitude in an acute triangle ABC. Points E,F are orthogonal projections of D on, respectively, AB,AC,. M,N are midpoints of, respectively, AB,AC. Lines MF,EN intersect at point S. Show that circumcenter of ABC lies on line SD.

I have no idea.

2. ## Re: difficult proof!

Do you understand what these words mean? Do you understand what the "orthogonal projection" of D on AB and AC means? Can you draw a picture showing them? Do you know what the "circumcenter" of ABC is?

3. ## Re: difficult proof!

of course, I drawed a picture

4. ## Re: difficult proof!

Originally Posted by TobiWan
of course, I drawed a picture
Good! Show us your drawing. Tell what methods are you expected to use?

5. ## Re: difficult proof!

at the beggining I tried to draw a line parallel to the SD from the point E, which intersects BC at G and made up sth from Thales'Theorem, but probably its not the way

6. ## Re: difficult proof!

generaly I would like to show that some points lie on a circle

7. ## Re: difficult proof!

should I show my drawing?