# Solution to the [[Semi-Circle in a Square II]] Puzzle +-- {.image} [[SemiCircleinaSquareII.png:pic]] > A semicircle in a square. What's the missing length? =-- ## Solution by [[Angle in a Semi-Circle]] and [[Symmetry]] of a [[Square]] +-- {.image} [[SemiCircleinaSquareIIlabelled.png:pic]] =-- With the points labelled as above, angle $A \hat{E} D$ is the [[angle in a semi-circle]] and so is $90^\circ$. Therefore, rotating the square by $90^\circ$ (either clockwise or anti-clockwise) rotates line segment $A B$ so that it is parallel to line segment $C D$. It also still runs between two sides of the square, since rotating the square leaves the square looking the same. Therefore, line segments $A B$ and $C D$ have the same length, and so the missing length is $25$.