A smooth circular cylinder of radius b is fixed parallel to a smooth vertical wall with its axis horizontal at distance c from the wall. A smooth uniform heavy rod of length 2a rests on the cylinder with one end on the wall in a vertical plane perpendicular to the wall. Show that its inclination θ to the horizontal is given by
acos3θ+bsin3θ=c
Please help
On thinking about this further, I wonder if the question is about using geometry to find the length of a line from a vertical wall to a tangent point on a circle, as per the figure below. If so, it's pretty easy to show that the length of that line is equal to the . Upon rearranging, and using 2a for the length of the rod, you get:
But this does not equal the formula provided in the question. For example, if theta = 0 then this formula yields c = 2a whereas the formula provided in the original question yields a=c.