Question 13
G4 (USA) Let $\triangle ABC$ be an equilateral triangle and let $P$ be a point in its interior. Let the lines $AP,BP,CP$ meet the sides $BC,CA,AB$ in the points $A_1,B_1,C_1$ respectively. Prove that
$$A_1B_1\cdot B_1C_1\cdot C_1A_1\ge A_1B\cdot B_1C\cdot C_1A.$$
$$A_1B_1\cdot B_1C_1\cdot C_1A_1\ge A_1B\cdot B_1C\cdot C_1A.$$