11.12. A cube with edge $a$ lies on a plane. A light source is located at a distance $b$ from the plane, where $b>a$. Find the minimum value of the area of the shadow cast by the cube on the plane.

## § 3. Distances
11.12. Let $A B C D$ be a square with side $a$; point $X$ is removed from the line $A B$ by a distance $b$, with $b > a$; $C'$ and $D'$ are the points of intersection of the extensions of segments $X C$ and $X D$ beyond points $C$ and $D$ with the line $A B$. Since $\triangle C' D' X$ is similar to $\triangle C D X$, then $x: b = a: (b-a)$, where $x = C' D'$. Therefore, $x = ab / (b-a)$. These considerations show that the shadow cast by the top face of the cube always represents a square with side $ab / (b-a)$. Consequently, the area of the shadow cast by the cube will be smaller when this shadow coincides with the shadow cast by the top face alone, i.e., when the light source is positioned above the top face. In this case, the area of the shadow is $(ab / (b-a))^2$; the bottom face of the cube is considered to be within the shadow.