Question 6
(CZS 1) For a triangle $ABC$, let $k$ be its circumcircle with radius $r$. The bisectors of the inner angles $A$, $B$, and $C$ of the triangle intersect respectively the circle $k$ again at points $A'$, $B'$, and $C'$. Prove the inequality
$$16Q^3\ge27r^4P,$$
where $Q$ and $P$ are the areas of the triangles $A'B'C'$ and $ABC$ respectively.
$$16Q^3\ge27r^4P,$$
where $Q$ and $P$ are the areas of the triangles $A'B'C'$ and $ABC$ respectively.