# Obviously AM GM

Geometry Level 3

Denote a variable $$a> 2$$ such that $$A,B,C$$ be three variable angles such that

$a \ \tan A + \sqrt{a^2+ 4 } \ \tan B + \sqrt{a^2 - 4} \ \tan C = 6a$

What is the minimum value of $$\tan^2 A + \tan^2 B + \tan^2 C$$?

×