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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.)
    Pythagoras would like this | Comment 9 of 15 |
    AC is 14.
    Just takes two applications of the Pythagorean Theorem:

    DC is 6 so DM is 5 and triangle MDA is a right triangle, so by the Pythagorean Theorem, MA is Square root of 75. But triangle MCA is also a right triangle, so by Pythagoras, AC^2 = 75 + 11^2. AC^2 = 196, so AC = 14.

      Posted by mark hartman on 2003-05-30 12:32:56
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