Let D be a point on side BC of triangle ABC.

If the incircles of triangles ABD and ACD are congruent, then what is the length of the cevian AD in terms of a, b, and c ?

If the cevian AD perpendicularly bisect BC...
Identifying cevian AD as d in the Pythogorean equations
  c^2 = d^2 + (a/2)^2   and   b^2 = d^2 + (a/2)^2
then adding the two equations together and moving the term d to one side of the equation gives the cevian AD equaling
SQRT(2b² + 2c² - a²)/2.

 

 

 

Edited on May 12, 2008, 8:14 pm

Posted by Dej Mar on 2008-05-12 01:11:00