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Found problems: 1

2011 Junior Balkan Team Selection Tests - Romania, 2
Tags: chapter 5
Let $A_1A_2A_3A_4A_5$ be a convex pentagon. Suppose rays $A_2A_3$ and $A_5A_4$ meet at the point $X_1$. Define $X_2$, $X_3$, $X_4$, $X_5$ similarly. Prove that $$\displaystyle\prod_{i=1}^{5} X_iA_{i+2} = \displaystyle\prod_{i=1}^{5} X_iA_{i+3}$$ where the indices are taken modulo 5.