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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.
  •   Submitted by Dulanjana    
    Rating: 2.9091 (11 votes)
    Solution: (Hide)
         DB = CB / 2 = 12 / 2 = 6
         MB = CB - CM = 12 - 11 = 1
         DM = DB - MB = 6 - 1 = 5
         DM^2 + AM ^2 = AD^2 (pythagorean), so
         25 + AM^2 = 100
         AM = sqrt(75)
         CA^2 = AM^2 + CM^2 (pythagorean), so
         CA = sqrt(75 + 121) = sqrt(196) = 14

    Comments: ( You must be logged in to post comments.)
      Subject Author Date
    re(2): Puzzle ResolutionK Sengupta2022-03-24 20:42:23
    re: Puzzle ResolutionAdy TZIDON2012-07-17 10:04:32
    SolutionPuzzle ResolutionK Sengupta2007-06-15 12:21:11
    answerK Sengupta2007-06-15 12:17:16
    Hints/Tipsre: Trouble with the solutionJim2005-10-14 20:38:26
    Trouble with the solutionB2004-12-03 17:10:04
    SolutionSolutionAntonio2003-09-04 07:28:26
    Pythagoras would like thismark hartman2003-05-30 12:32:56
    solutionrob allen2003-02-04 09:09:59
    PythagorasMichael2003-02-02 23:33:45
    re(2): Why Angle A?TomM2002-07-01 10:03:34
    re: Why Angle A?levik2002-07-01 09:37:18
    2 + 2 = 5 Doh!TomM2002-07-01 08:49:31
    QuestionWhy Angle A?TomM2002-07-01 08:41:18
    SolutionSolutionfriedlinguini2002-07-01 06:21:07
    Some Thoughtstry..Cheradenine2002-07-01 05:10:22
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