Calculating the radius of a circle - simple trigonometry/geometry

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?

Re: Calculating the radius of a circle - simple trigonometry/geometry

Hey Mukilab.

I don't know what triangle you are referring to, but it isn't in any way reflecting the radius of the circle. What the video did is the best way to figure out the problem IMO.

Re: Calculating the radius of a circle - simple trigonometry/geometry

Ah nevermind, I started drawing the circle/triangle on paint and I realised my mistake.

Thank you for taking the time to post anyway :)