Question 67
Determine all triples $(a, b, c)$ of real numbers such that
$$
a^2 + b^2 + c^2 = 1 \quad \text{and} \quad (2b - 2a - c)a \ge \frac{1}{2}. \quad \text{(Ivan Kokan)}
$$
$$
a^2 + b^2 + c^2 = 1 \quad \text{and} \quad (2b - 2a - c)a \ge \frac{1}{2}. \quad \text{(Ivan Kokan)}
$$