I assume the word "point" in red above is supposed to be "circle."
We can write the equation for the circle and equation for the line, and now we are solving a system of two equations in two variables, where one equation is quadratic and the other linear.
For example, a unit circle centered at the origin, whose equation is , and the points and defining the line .
Substitute the value of into the first equation to get
Now we have a quadratic equation in one variable, and we can solve for .
The reasoning for rectangles or other shapes is similar, except that we might not have a tidy equation to work with. Depending on the circumstances, we might elect to use approximation techniques instead.