Prove that $AC^2 + BD^2+ 4PQ^2 = AB^2 +BC^2+ CA^2+DA^2$

Question

In a quadrilateral $ABCD$ in which $P$ and $Q$ are the midpoints of $AC$ and $BD$. Prove that $AC^2 + BD^2+ 4PQ^2 = AB^2 +BC^2+ CA^2+DA^2$

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Answer 1

Hint Use the formula for the midline in triangles $QAC, ABD, CBD$