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Sum Projection Differences (Posted on 2008-01-05) Difficulty: 3 of 5

Let ABC be an arbitrary triangle.

Let AB and AC be the orthogonal projections of A onto the internal bisectors of angles B and C respectively.

Let BC and BA be the orthogonal projections of B onto the internal bisectors of angles C and A respectively.

Let CA and CB be the orthogonal projections of C onto the internal bisectors of angles A and B respectively.

Prove that |ABAC| + |BCBA| + |CACB| = s,

where s is the semiperimeter of triangle ABC.

See The Solution Submitted by Bractals    
Rating: 2.0000 (3 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionNice puzzle!Chesca Ciprian2008-01-07 15:49:37
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