Experiment with a GSP animation? Yes.
Can you find any special cases? What if P lies on the angle bisector? If P is not on the angle bisector, can you find reasons why the isosceles triangle is not the one with minimal area?
Note: Here is a case where GSP can probably generate pretty good intuition about what line will minimize the area of triangle AOB but not yield much insight on how to construct it or even to prove that it is the line generating the minimal area. Is the line unique?