How do you find the incenter of a triangle algebraically?
It depends upon what information you are given that defines a unique triangle. You could be given the lengths of the three sides, the length of two sides and the included angle, or two angles and the included side. In any event you can compute the all the remaining parts of the triangle if you are given one of the above. You can compute the area and the perimeter. Then the inradius is computed by r = A/s where r is the length of the inradius, A is the area of the triangle and s is the semiperimeter of the triangle.
