From the circle detailed in this video:

Edexcel Core Maths C2 June 2011 Q5b : ExamSolutions - YouTube

To find the radius of the inner circle, why cannot we take the line down from OC to form a right angled triangle, and then do

tan(pi/6)=r/6?

Since tan is opposite over adjacent, why would this not work?

Apparently the answer is r=2, that's now what you would get doing the above. Why is it wrong?