1999 AIME Problem 12

The inscribed circle of triangle ABC is tangent to \overline{AB} at P_{}, and its radius is 21. Given that AP=23 and PB=27, find the perimeter of the triangle.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.