In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction.

Answer 1

Triangle $\triangle ACX$ is divided into two right triangles: $\triangle ACB$ and $\triangle BCX$, so the ratio of the area of $\triangle BCX$ to the area of $\triangle ACX$ is the same as the ratio of the leg of the right triangle $\triangle BCX$ to the hypotenuse of the right triangle $\triangle ACX$. Therefore, the ratio of the areas is $\boxed{\frac12}$.