Question 138
Given a triangle $ABC$, let $A'$ be the reflection of $A$ in $C$, $A''$ the reflection of $A$ in $B$, $B'$ the reflection of $B$ in $A$, $B''$ the reflection of $B$ in $C$, $C'$ the reflection of $C$ in $B$ and $C''$ the reflection of $C$ in $A$ (each reflection being the point symmetric with respect to the given point). Determine the ratio between the area of $A'B'C'$ and that of the hexagon $A'A''C'C''B'B''$.
(A) $\frac{6}{13}$
(B) $\frac{7}{13}$
(C) $\frac{3}{7}$
(D) $\frac{1}{2}$
(E) It depends on the initial triangle.
(A) $\frac{6}{13}$
(B) $\frac{7}{13}$
(C) $\frac{3}{7}$
(D) $\frac{1}{2}$
(E) It depends on the initial triangle.