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Angle Bisectors (Posted on 2008-02-11) Difficulty: 3 of 5
In triangle ABC, angle C has a measure of 60 degrees. Point D lies on side AC so that BD bisects angle B and BD = 1. Similarly, point E lies on side BC so that AE bisects angle A and AE = 2.

Find the area of triangle ABC.

See The Solution Submitted by Dennis    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 5

It is easy to verify that if B is a right angle,
then |AE| = 2|BD|.
Applying the law of sines to triangle BCD gives,
     |BC|        |BC|         |BD|          1
  --------- = ---------- = ---------- = ---------
   sin(75)     sin(BDC)     sin(BCD)     sin(60)
            or
          sin(75)
  |BC| = ---------
          sin(60)
Therefore,
 
  Area(ABC) = (1/2)|AB||BC| = (1/2)|BC|^2*tan(60)
               sin(75)^2
            = ----------- ~= 1.07735
                sin(60)
 

  Posted by Bractals on 2008-02-11 13:41:41
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