December 1st, 2011, 04:32 AM  #1 
Member Joined: Dec 2011 Posts: 61 Thanks: 0  perimeter
The triangle ABC has sides of length a,b and c.Show that perimeter of triangle ABC satisfies p^2 = 2bc(1 + cos A) + 2ac(1 + cos B) + 2ab(1 + cos C) 
December 1st, 2011, 05:14 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: perimeter
The perimeter p is p = a + b + c. By the law of cosines, we may state: Adding, we get: Add 2ab + 2ac + 2bc to both sides: 

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