Sorry if this question is a tad poorly written, as I don't have much of a mathematical background and am actually a costume designer who's in a bit of a pinch. I have been trying to create an eye shape for one of my costumes, and have found out that it can be defined by a tangent circle within a lens shape. The lens shape I have been able to draw out easily, but adding the tangent circle is giving me somewhat of a problem.
I am intending it to be of a given radius, and be internally tangent to both of the circles defining the lens. I've managed to figure out that the radius of this type of circle can actually be calculated, so I would venture a guess that the reverse is plausible. How do I construct this in a way that ensures the tangent circle has the radius I would like?
To draw tangent circles, the tangent point and the two centers must be colinear. Suppose that the lents have radius R and the circle you want to inscribe has radius r. Draw a circle of radius R-r and center it on the same point you have centered each lent. The two intersections of that circles are the center of the circle you want.
That is because when you draw a circle at this point, the maximum distance for the center of a lent you will get is presicely R, so they are tangent. Similarly, if one center of a lent is radius R and the other R', one circle must be of radius R-r and the other R'-r. If the lents are not circles and are, for example, elipses, there are other method a bit longer. Tell me if you want that method.