VTMO 2020 — Grade 9 — vtmo Question 10

Question 10

Positive $a , b , c$ satisfy a $^{2} + b^{2} + c^{2} = 3$. Find the smallest $k$ such that $\min \left(a + b , b + c , c + a\right) \gt k$ guarantees a triangle.

$1$
$\sqrt{3}$
$\frac{3}{2}$
$\sqrt{2}$
$2$