...py2 = 1
Inner circle: (px-cx)2 + (py-cy)2 = py2
Tangent condition: {-py, px} . eps2 . {-(py-cy), (px-cx)} = 0
where eps2 is the 2D antisymmetric symbol {{0,1},{-1,0}}.
The solution:
px = 2*cx/(1+cx2)
py = (1-cx2)/(1+cx2)
cy = (1/2)*(1-cx2)
The center of the inner circle is thus on a...