Question 8
In triangle $ABC$, $\angle ACB=45^\circ$ and $BC=24$ cm. The length of the altitude from $A$ to $BC$ is $16$ cm. Points $B^\prime$ and $C^\prime$ are on the line of $BC$ such that $BC=B^\prime C^\prime$. Suppose $AB=A^\prime B^\prime$ and $AC=A^\prime C^\prime$, as shown in the diagram below. If the area of triangle $OCC^\prime$ is $\frac13$ of the area of triangle $ABC$, what is the length, in cm, of $BB^\prime$?
