Question 1
Let $ABC$ be an arbitrary triangle. Arbitrary points $C_1$, $A_1$ and $B_1$ are chosen on the sides $AB$, $BC$ and $CA$ respectively. Let $P_1$, $P_2$ and $P_3$ denote the areas of triangles $AC_1B_1$, $BC_1A_1$ and $CA_1B_1$ respectively, and let $P$ denote the area of triangle $ABC$. Prove that $\sqrt{P_1} + \sqrt{P_2} + \sqrt{P_3} \le \frac{3}{2}\sqrt{P}$.