Heron's Formula for Area, then used to find inradius
- Kevin Hopkins
Heron's Formula, explained at https://math.stackexchange.com/questions/1082958/how-to-find-the-inradius-of-a-triangle-with-given-side-lengths can be used to find the area of any triangle. Slice the triangle into 3 smaller triangles by connecting each vertex to the incenter, and you can see a relationship between the inradius and the area and perimeter of the triangle. A problem like this appeared on the AHSME in 1950: http://artofproblemsolving.com/wiki/index.php?title=1950_AHSME_Problems/Problem_35. Here are some problems for practicing this. It is not asked, but you should also be able to find each altitude of the triangle once you can find its area.