(a) equilateral
a2 + b2 + c2 = ab + bc + ca
⇒ a2 + b2 + c2 – ab – bc – ca = 0
⇒ 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0
⇒ (a – b)2 + (b – c)2 + (c – a)2 = 0
Sum of perfect squares = 0 ⇒ Each term of the sum is zero
⇒ (a – b) = 0 = (b – c) = (c – a)
⇒ a = b = c
⇒ The triangle is equilateral.