Proving that ABC is an equilateral triangle
Source: Romanian NMO 2007, 7th grade, problem nr. 1
July 11, 2008
Problem Statement
In a triangle , where a \equal{} BC, b \equal{} CA and c \equal{} AB, it is known that: a \plus{} b \minus{} c \equal{} 2 and 2ab \minus{} c^2 \equal{} 4. Prove that is an equilateral triangle.