Question 1062307: How can I draw a triangle when the lengths of three angle bisectors are given? Will the length of angles bisectors determine the triangle?
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
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:
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.
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).
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