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Math Help - Distances in a right triangle

  1. #1
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    Distances in a right triangle

    ABC is a right triangle with ABC=90 with AB=30 sqrt 3and BC=30. D is a point on segment BC such that AD is the median. E is a point on segment AC such that BE is perpendicular to AC. AD and BE intersect at F. If EF=(a sqrt b)/c, where aand c are positive, coprime integers and b is not divisible by the square of any prime, what is the value of a+b+c?
    Last edited by geniusgarvil; March 31st 2013 at 11:34 PM.
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  2. #2
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    Re: Distances in a right triangle

    The triangle ABC is 30,90,60 triangle....with BE as height and AD as median...angle BAD is easy to calculate so does the angle FAE.. AC = 60 ,AE = 45 and EC = 15 .
    You have whatever you need to find EF.....then compare it with what you have....just elementary algebra..
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  3. #3
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    Re: Distances in a right triangle

    Hi,
    Everything in the previous posting is certainly true, but I don't see how this immediately gives the distance EF. Here is a purely algebraic solution:

    Distances in a right triangle-mhfgeometry22.png
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