Question 1062307
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How can I draw a triangle when the lengths of three angle bisectors are given? Will the length of angles bisectors determine the triangle?
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The answer to your first question is:


<pre>
     It is NOT POSSIBLE to construct a triangle using a compass and straightedge if the givens are the lengths of its three angle bisectors.


    In other words, such an algorithm DOES NOT exist for the general case.
</pre>

It was proved in Russian sources by very authoritative mathematician, and the links in the Internet are on Russian articles. See, for example, 

http://www.mccme.ru/ask/qa/bissect.html 



I don't know the references in English (although they should be, I believe).



Regarding your second question, see this reference


Mironescu, Petru; Panaitopol, Laurentiu "The existence of a triangle with prescribed angle bisector lengths." 
American Math. Monthly, 101, No.1, 58-60 (1994).