Question 31
Let $ABC$ be a triangle and let $A'$ be the symmetric of $A$ with respect to $BC$; then let $DAA'$ be similar to $ABC$ and let $D'$ be the symmetrical of $D$ with respect to $AA'$. Knowing that the product of the areas of the quadrilaterals $ABA'C$ and $ADA'D'$ is $16$, we can say that $AA'$ ...
(A) is $1$
(B) is $2 \sqrt[4]{2}$
(C) is $2$
(D) is $2 \sqrt{2}$
(E) is not uniquely determined by the data. (Note: the similarity between $DAA'$ and $ABC$ must be understood in an orderly way: $DA/AB = AA'/BC = A'D/CA$ )
(A) is $1$
(B) is $2 \sqrt[4]{2}$
(C) is $2$
(D) is $2 \sqrt{2}$
(E) is not uniquely determined by the data. (Note: the similarity between $DAA'$ and $ABC$ must be understood in an orderly way: $DA/AB = AA'/BC = A'D/CA$ )