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The lengths of the sides of a triangle are a, b and c respectively. If a² + b² + c² = ab + bc + ca, then the triangle is :
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- isosceles
- equilateral
- scalene
- right-angled
- isosceles
Correct Option: B
Here , a² + b² + c² = ab + bc + ca
⇒ 2a² + 2b² + 2c² = 2ab + 2bc + 2ca
⇒ a² + b² – 2ab + b² + c² – 2bc + c² + a²– 2ca = 0
⇒ (a – b)² + (b – c)² + (c – a)² = 0
∴ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c
∴ It is an equilateral triangle.
