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Thread: difficult proof!

  1. #1
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    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.
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  2. #2
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    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?
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  3. #3
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    Re: difficult proof!

    of course, I drawed a picture
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  4. #4
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    Re: difficult proof!

    Quote Originally Posted by TobiWan View Post
    of course, I drawed a picture
    Good! Show us your drawing. Tell what methods are you expected to use?
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  5. #5
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    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
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  6. #6
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    Re: difficult proof!

    generaly I would like to show that some points lie on a circle
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  7. #7
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    Re: difficult proof!

    should I show my drawing?
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  8. #8
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    Re: difficult proof!

    difficult proof!-screenshot_2016-11-26-13-20-35.png
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