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Perimetre egale

 
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Claudiu Mindrila
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Joined: 01 Oct 2007
Posts: 557
Location: Targoviste

PostPosted: Sun Jan 04, 2009 7:55 pm    Post subject: Perimetre egale Reply with quote

Problema. Fie ABC un triunghi oarecare cu AD bisectoarea unghiului \angle BAC. Sa se demonstreze ca daca triunghiurile ABD si ACD au perimetre egale atunci AB=AC.
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Euclid


Joined: 30 Nov 2008
Posts: 23
Location: Babadag

PostPosted: Sun Jan 04, 2009 8:31 pm    Post subject: Reply with quote

AB+AD+BD=AC+AD+CD \Leftrightarrow AB+BD=AC+CD

Presupunem ca DB<DC sau DB>DC sau DB=DC

DB<DC \Leftrightarrow AC>AB \Leftrightarrow AB+BD<AC+CD

DB>DC analog

DB=DC \Leftrightarrow AC=AB \Leftrightarrow AB+BD=AC+CD
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