Question 182
Let $ABCD$ be a given convex quadrilateral. Determine the locus of the points $P$ lying inside the quadrilateral $ABCD$ and satisfying
$$
[PAB] \cdot [PCD] = [PBC] \cdot [PDA],
$$
where $[XYZ]$ denotes the area of triangle $XYZ$.
$$
[PAB] \cdot [PCD] = [PBC] \cdot [PDA],
$$
where $[XYZ]$ denotes the area of triangle $XYZ$.