Notes
overlapping square and circle solution

Overlapping Square and Circle

Solution by Intersecting Chords Theorem

Let $x$ be half the side length of the square. Then $C P$ and $P D$ both have length $x$, while $A P$ has length $2 x$. Applying the intersecting chords theorem shows that $1 \times 2 x = x \times x$ so $x = 2$. The side length of the square is then $4$, so its area is $16$.