# Overlapping Square and Circle +-- {.image} [[OverlappingSquareandCircle.png:pic]] > What's the area of the square? =-- ## Solution by [[Intersecting Chords Theorem]] +-- {.image} [[OverlappingSquareandCircleLabelled.png:pic]] =-- 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 $16$.