The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices using the side lengths of the triangle relative to the perimeter (that is, using the barycentric coordinates given above, normalized to sum to unity) as weights. The weights are positive so the incenter lies inside the triangle as stated above. If the three vertices are located at formula_32, formula_33, and formula_34, and the sides opposite these vertices have corresponding lengths formula_7, formula_9, and formula_11, then the incenter is at