Alright... so I thought of this problem on the train ride home. I am sure plenty thought of it before me...but now it is my turn.
Say want to know what the length L an equilateral triangle must have such that all three points touch the circle of radius R that it is contained by.
I have drawn the problem. i have bisected one of the 60 degree angles to form a right triangle.
I then drew a line perpendicular to the bisecting line to create a similar triangle.
I do not know if this is the way you would have approached this, but it seemed pretty logical to me.
I feel like I have almost all (if not all) the necessary info to write L in terms of R.
Can someone chime in with a hint here?
I feel like I need something more about either the short leg of the inner triangle or its hypoteneuse. then I can relate
both triangles to the angle.