Isosceles triangle enigma
Name: brian reynolds
Date: Around 1995
I have a geometry question that has been plaguing me since I was in high
school when it was given as an extra credit problem. The problem is: given
a diagram that looks like an isosceles triangle the segments that are formed
by the two "base" angle bisectors and the sides opposite the angles are
given to be congruent in length. Given only that these segments, which
happen to bisect these angles and terminate on the legs, are equal in
length--prove that the triangle is indeed isosceles.
The guys here in the lab have been puzzling over this one for days now;
nobody can come up with a geometric proof. However, using trigonometry it
is pretty simple: apply the Law of Sines to the two triangles formed by the
angle bisectors and the apex of the main triangle.
Sorry about that. It is actually pretty complicated, but it can,
indeed, be proven using law of Sines. We will continue to look for
a geometric proof.
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Update: June 2012