Question 1105372
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If  {{{a^2 + b^2 + c^2}}} = ab + ac + bc,  then


{{{2*(a^2 + b^2 + c^2)}}} = 2*(ab + ac + bc),   or,  equivalently,


{{{(a-b)^2 + (a-c)^2 + (b-c)^2}}} = 0,


which implies  a = b,  a = c  and  b = c.


Hence, the triangle is  <U>EQUILATERAL</U>.
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