type of triangle

[Vali]

I have a triangle ABC and I know that \(\displaystyle tan(\frac{A}{2})=\frac{a}{b+c}\) then this triangle is:
a. equilateral
b. right triangle with A=pi/2
c. right triangle with B=pi/2 or C=pi/2
d. acute
e. obtuse
a,b,c are the sides opposite of the angles A,B,C
How to start?

 

[Dr.Peterson]

I don't quickly see an answer using theorems I have memorized; but the equation reminds me of the Law of Tangents, as well as other formulas involving tangents of half angles in a triangle. Have you learned any of these less-well-known facts, such that you might be expected to recognize it on sight?

In the absence of such a specialized trick, I would probably start with the half-angle formula for the tangent. In fact, having just tried that out, I see the answer quickly.

Show us some work using this idea.

 

[Vali]

I did it.Thanks!