6. [6] Let $A B C$ be a right triangle with hypotenuse $A C$. Let $B^{\prime}$ be the reflection of point $B$ across $A C$, and let $C^{\prime}$ be the reflection of $C$ across $A B^{\prime}$. Find the ratio of $\left[B C B^{\prime}\right]$ to $\left[B C^{\prime} B^{\prime}\right]$.
Answer: 11 Solution: Since $C, B^{\prime}$, and $C^{\prime}$ are collinear, it is evident that $\left[B C B^{\prime}\right]=\frac{1}{2}\left[B C C^{\prime}\right]$. It immediately follows that $\left[B C B^{\prime}\right]=\left[B C^{\prime} B^{\prime}\right]$. Thus, the ratio is 1 .