# Solution to the Two Semi-Circles and a Rectangle Puzzle +-- {.image} [[TwoSemiCirclesandaRectangle.png:pic]] > A horizontal line of length $8$ joins these semicircles. What's the area of the rectangle? =-- ## Solution by the [[Intersecting Chords Theorem]] +-- {.image} [[TwoSemiCirclesandaRectangleLabelled.png:pic]] =-- With the points labelled as above, let $a$ be the length of $A P$ and $b$ the radius of the smaller semi-circle, so the length of $B P$. The area of the rectangle is then $a b$. Applying the [[intersecting chords theorem]] to $A P$ and $C P$ shows that $a b = 8^2$. So the area of the rectangle is $64$.