VTMO 2026 - Grade 9 - Semifinal - SET 05 - Self-study Question 10

Question 10

For positive real numbers $a,b,c$ with $a^2+b^2+c^2=3$, find the smallest real $k$ such that $\min\{a+b,b+c,c+a\}\gt k$ guarantees that $a,b,c$ are side lengths of a triangle.

1
$\sqrt3$
$3/2$
$\sqrt2$
2