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Perpendicular Incenters (Posted on 2018-05-06) Difficulty: 3 of 5

  
Let a, b, and c be the lengths of sides BC, CA, and AB respectively
of ΔABC. Let D be a point on side BC. Let I and J be the incenters
of ΔABD and ΔACD respectively.

If the line segment IJ ⊥ AD, then what is the value of the ratio
|BD| / |CD| in terms of a, b, and c?
  

See The Solution Submitted by Bractals    
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