Prove the inequality?

Let a = mc and b = nc.
a^2 + b^2 + c^2 - c(a + b)
= (m^2 + n^2 + 1)c^2 - c^2(m + n)
= c^2(m^2 + n^2 - m - n + 1)
= c^2((m - 1/2)^2 + (n - 1/2)^2 + 1/2)
c^2 is non-negative and (m - 1/2)^2 + (n - 1/2)^2 + 1/2 is positive,
so a^2 + b^2 + c^2 - c(a + b) is non-negative.
Therefore, a^2 + b^2 + c^2 ≧ c(a + b).