Question 14
Let $P$ be a point in the interior of a triangle $ABC$. Through $P$ the parallels $KP$, $MP$ and $NP$ to the sides $AB$, $AC$ and $BC$ are drawn, which divide the original triangle into three triangles and three parallelograms. Let $S_{1}$, $S_{2}$, $S_{3}$ be the areas of the new triangles and $S$ the area of the triangle $ABC$. Prove that
$$
S \leq 3\left(S_{1}+S_{2}+S_{3}\right)
$$
$$
S \leq 3\left(S_{1}+S_{2}+S_{3}\right)
$$