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The Unknown Side (Posted on 2002-07-01) Difficulty: 3 of 5
ABC is a triangle:
  • Angle A < 90.
  • D is a point on BC such that BD = DC.
  • M is a point on BC such that AM is perpendicular to BC.

    If
  • AD = 10,
  • BC = 12 and
  • MC = 11
    find the length of AC.
  • See The Solution Submitted by Dulanjana    
    Rating: 2.9091 (11 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Solution Puzzle Resolution | Comment 14 of 15 |
    (In reply to answer by K Sengupta)

    MB = BC-MC = 12-11 = 1
    BC = 12, and so: BD = DC =6
    Thus, DM = DB - MB = 6-1=5

    Accordingly, AM = V(10^2 - 5^2) = V(75)

    But MC = 11, and so:
    AC = sqrt(AM^2 + MC^2)
    = sqrt(75+121)
    = sqrt(196)

     


      Posted by K Sengupta on 2007-06-15 12:21:11
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