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Let $C_1,C_2,C_3,C_4$ be compact convexes of $\mathbb{R}^2$ such that $C_1\cap C_2\cap C_3\neq\emptyset,C_1\cap C_2\cap C_4\neq\emptyset,C_1\cap C_3\cap C_4\neq\emptyset,C_2\cap C_3\cap C_4\neq\emptyset$.
Show that $C_1\cap C_2\cap C_3\cap C_4\neq\emptyset$
Let $C_1,\dots,C_n$ be compact convex...