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OBMJ 2011 Problema 4

 
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PhantomR
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Joined: 20 Mar 2011
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PostPosted: Sat Jul 02, 2011 7:34 pm    Post subject: OBMJ 2011 Problema 4 Reply with quote

Problema 4. Fie ABCD un patrulater convex. Fie E şi F puncte de pe laturile AB şi CD, respectiv, astfel că AB:AE=CD:DF=n. Dacă S este aria patrulaterului AEFD, demonstraţi că
S\leq{\frac{AB\cdot{CD}+n(n-1)DA^2+nDA\cdot BC}{2n^2}}.
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