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forum.virtualchallengemeets.com • View topic - 2010 USAMO 1/USAJMO 3

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2010 USAMO 1/USAJMO 3

Posted: Wed May 05, 2010 5:44 am

by stupidityismygam

Let [unparseable or potentially dangerous latex formula] be a convex pentagon inscribed in a semicircle of diameter [unparseable or potentially dangerous latex formula]. Denote by [unparseable or potentially dangerous latex formula] the feet of the perpendiculars from [unparseable or potentially dangerous latex formula] onto lines [unparseable or potentially dangerous latex formula] respectively. Prove that the acute angle formed by lines [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] is half the size of [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] is the midpoint of segment [unparseable or potentially dangerous latex formula].