A box in the shape of a triangle with side lengths \(13\), \(14\), and \(15\) is being used to pack a pizza pi. The pizza is in the shape of a circle and just touches each of the three sides of the triangular box. What is the area of the circle?
Note: For this problem, the following known results about circles may be useful:
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
If two tangent segments are drawn to a circle from a point outside of the circle, then the lengths of those segments are equal.
