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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.)
    re(2): Why Angle A? | Comment 6 of 15 |
    (In reply to re: Why Angle A? by levik)

    On giving it more thought, I realized that if Angle C were obtuse, then in the right triangle AMD, the leg MD (17) would be longer than the hypotenuse AD (10), which is impossible. So the assumption that angle C is acute is verified.

    It still brings up the question why irrelevant information about angle A was mentioned in the initial conditions of the problem.
      Posted by TomM on 2002-07-01 10:03:34

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