Problem 357. Square, Exterior point, Triangles, Area
Level: High School, College, SAT Prep.

The figure shows a square ABCD of area
S with an exterior point P. If S_{1}, S_{2}, S_{3},
and S_{4}, are the areas of triangles PAB, PBC, PCD, and
PAD, respectively, prove that S_{1} + S_{3} = S_{2}
- S_{4} = S/2.