Two circles when passing through two fixed points on x-axis (red, purple) are shown enclosing $80^{\circ}, 100^{\circ}$ approximately at any two points on their chords.
How is it possible to find any of each of equations of any two continuously differentiable non-circular curves ( analytical or in differential form) passing through the given points such that the sum of varying subtended angles at C,D is always $180^{\circ}$?
