Given a triangle circumscribed about a circle (or, a circle inscribed within a triangle), there are three points of tangency.
The segments between the vertex and two points of tangency are congruent, so they have the same length. So, by examining the segments created between a vertex and each point of tangency, it is possible to know the lengths of each segment from a vertex and point of tangency. Recall that the perimeter of a polygon is the sum of the lengths of each side. This is the same as adding the value of each segment. Thus, by doing so, you have found the perimeter of the triangle.