Question: Circle of maximum radius inscribed between curves

The problem arose while playing with inscribed circles, as in this post. If anyone is interested, try to find a circle of maximum radius inscribed between the curves
x1^2 + 2*x2^2 - 1 = 0 and (x1 - sin(x1))^2 + (x2 - sin(x2))^2 - 1 = 0.

Curve graphs.

 

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