Question 26
Let $ABC$ be a triangle and $X$, $Y$, $Z$ points on the sides $BC$, $AC$, $AB$ respectively. Let $A'$, $B'$, $C'$ be the circumcenters of the triangles $AZY$, $BXZ$, $CYX$ respectively. Prove that
$$
(A'B'C') \geq \frac{(ABC)}{4}
$$
$$
(A'B'C') \geq \frac{(ABC)}{4}
$$