If a, b, c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is
Explanation:
a, b, c are the sides of a triangle.
It is given that a2 + b2 + c2 = bc + ca + ab
⇒ a2 + b2 + c2 - bc - ca - ab = 0
⇒ 2a2 + 2b2 + 2c2 - 2bc - 2ca - 2ab = 0
⇒ (a2 -2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2) = 0
⇒ (a - b)2 + (b - c)2 + (c - a)2 = 0
This is possible only if a = b = c
i.e., the triangle is equilateral.
Hence, option (a).
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