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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.

  • 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.)
    Trouble with the solution | Comment 11 of 15 |

    If ABC is a right triangle, the hypotnuse must always be larger then the length of either legs.  SO for ABC:


    But BC=12 and the solution for AC is 14?  This can't be true for a real triangle. 

    Another approach to the problem yields a different answer.

    Triangles ABC and MAC are similar because:

    angle BAC= angle AMC= 90

    Angle BCA= Angle ACM

    Therefore:  (AC/CM)=(BC/AC) or AC^2=BC*CM

    BC=12 and CM =11 so AC^2= 12*11=132

    AC=sqrt132 =(approx) 11.5


    Now, why don't both answers agree??????

      Posted by B on 2004-12-03 17:10:04
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