Found problems: 4
2013 Dutch IMO TST, 5
Let $a, b$, and $c$ be positive real numbers satisfying $abc = 1$.
Show that $a + b + c \ge \sqrt{\frac13 (a + 2)(b + 2)(c + 2)}$
2013 Dutch IMO TST, 5
Let $a, b$, and $c$ be positive real numbers satisfying $abc = 1$.
Show that $a + b + c \ge \sqrt{\frac13 (a + 2)(b + 2)(c + 2)}$
2012 Dutch Mathematical Olympiad, 1
Let $a, b, c$, and $d$ be four distinct integers.
Prove that $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ is divisible by $12$.
2008 Dutch Mathematical Olympiad, 4
Three circles $C_1,C_2,C_3$, with radii $1, 2, 3$ respectively, are externally tangent.
In the area enclosed by these circles, there is a circle $C_4$ which is externally tangent to all three circles.
Find the radius of $C_4$.
[asy]
unitsize(0.4 cm);
pair[] O;
real[] r;
O[1] = (-12/5,16/5);
r[1] = 1;
O[2] = (0,5);
r[2] = 2;
O[3] = (0,0);
r[3] = 3;
O[4] = (-132/115, 351/115);
r[4] = 6/23;
draw(Circle(O[1],r[1]));
draw(Circle(O[2],r[2]));
draw(Circle(O[3],r[3]));
draw(Circle(O[4],r[4]));
label("$C_1$", O[1]);
label("$C_2$", O[2]);
label("$C_3$", O[3]);
[/asy]