If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is Choose the correct choice from the following choices.
A) equilateral
B) isosceles
C) right-angled
D) obtuse-angled
E) None of these
Explanation :   We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac   Now assume values of a, b, c and substitute in this equation to check the options.   Shortcut:   (a – b)2 + (b – c)2 + (c – a)2 = 0.   Hence, a = b = c.   equilateralnswer : equilateral
<result>A</result>
If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is