How to inscribe a ball into a cone? If I position a ball into a cone at the deepest position possible, cut a plane centric through that 3D object and just look at that plane, then I assumed that: a) From the tangent points, the two lines running perpendicular from the tangents roughly towards the center of the ball (center of the circle, as seen in the plane) will cross exactly in the center of the ball (circle). b) The distance between the vertex of the cone and the center of the ball could thus be calculated as: d = ballradius / sin(halfconeangle). I now have to assume that something in my assumptions a) and b) is faulty (read about my doubts below). Are my assumptions correct? Would you know how to describe the geometrical situation correctly?
About my doubts: I have several examples drawn on paper, and measured “d”. But I measure different values than calculating them, and the error is getting bigger and bigger for smaller and even smaller angles. While there seems to be no obvious mismatch for drawings with a 60º, 40º,30º and 15º half cone angle and a 5.2 cm ball radius (all mismatches could be appointment to my drawing not being really exact), for a radius of a circle of about 1.1 cm and a half cone angle of 15º, 7.5º and 3.75º the error is already about 0.8 cm, 1 cm and 2 cm, an error so big that I exclude that my drawing would be sketched so bad. Actually, I was programming in MATLAB, and see such mismatch also there, but considering MATLAB I also would have to be sure that my code is correct. Indeed, observing such mismatch in the graphs drawn by my little MATLAB code, I suspected a failure in my MATLAB code and went for the classical paper method to first confirm that my assumptions a) and b) are correct. Now it looks as if my MATLAB code and my drawing might not be the problem, but the paper work suggests, that my math knowledge is bad. I am lost, and would really appreciate your help.