Circle within a drop

Question

How to create a program in mathematica that automatically adjusts a perfect circle inside the drop shape so that the outside parts of the circle are added part by part and returns us a value? As in the attached figure.

Droplet example

Answer 1

With reference to https://mathworld.wolfram.com/TeardropCurve.html

Manipulate[Show[{
   ParametricPlot[{Cos[t], Sin[t] Sin[t/2]^3}, {t, 0, 2 Pi}],
   ParametricPlot[{x Cos[t] - (1 - x), x Sin[t]}, {t, 0, 2 Pi}]}],
 {x, 0, 1}]