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 ?

(In reply to Solution by Dej Mar)

I need some clarification in your solution. First, I do not understand what you mean about the two incircles being congruent with triangle ABC. How is a circle congruent with a triangle.

Secondly, if cevian AD was the perp bisector of BC and the incircles of ABD and ACD were congruent, wouldn't this force ABC to be an isosceles triangle with congruent sides AB and AC?

Edit: It might indeed be the case that AD is the perp bisector of BC in order for this situation to occur, but I would need something more of a proof to establish this, and even then, your formula would simplify in that it would only need to be written in terms of 2 of the three sides.

Edited on May 12, 2008, 11:30 am

Posted by Mike C on 2008-05-12 11:27:29