For a triangle
let
be its circumcircle with radius
The bisectors of the inner angles
and
of the triangle intersect respectively the circle
again at points
and
Prove the inequality
where
and
are the areas of the triangles
and
respectively.
%V0
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
$$16Q^3 \geq 27 r^4 P,$$
where $Q$ and $P$ are the areas of the triangles $A'B'C'$ and $ABC$ respectively.
Školjka