# Solution to the Three Squares Overlapping a Semi-Circle Puzzle +-- {.image} [[ThreeSquaresOverlappingaSemiCircle.png:pic]] > The two smaller squares each have area $4$. What's the area of the larger square? =-- ## Solution by [[Intersecting Chords Theorem]] +-- {.image} [[ThreeSquaresOverlappingaSemiCircleLabelled.png:pic]] =-- As $A P$ is at right-angles to the diameter of the semi-circle, it is a [[tangent]] to it at $A$. The [[intersecting chords theorem]] then says that: $$ A P^2 = P C \times P D $$ Each small square has area $4$ so has side length $2$. Therefore $P C$ has length $2$ and $P D$ length $4$. Hence the area of the red square is $2 \times 4 = 8$.