Question 7
As shown in the diagram below, $ABCD$ is a convex quadrilateral with diagonals intersecting at point $P$. The sum of the areas of triangles $PAB$ and $PCD$ equals the sum of the areas of triangles $PAD$ and $PCB$. If $Q$ is the midpoint of $AC$ and $Q$ does not coincide with $P$, what is the value of $\frac{BP}{DP}$?
