An algebra problem by Ossama Ismail

Algebra Level 3

If $a,$ $b,$ and $c$ are real numbers such that $a^2 + b^2 + c^2 = 1,$ then what is the minimum value of $ab + bc +ca?$

-1

- \frac{2}{3}

- \frac{1}{2}

-\frac{1}{4}

\frac{1}{4}

\frac{1}{2}

1