Consider the inversion which interchanges line (p) with circe (c). Its circle (q) is centered at Q and its radius satisfies r

Some other relations here are worth noticing:

[1] The inversion maps the circumcircle (d) of triangle QIJ to line CD. Thus (q) and (d) intersect on line ACD.

[2] The intersection point E of (c) and (d) maps by the inversion to A (intersection of CD and (p)).

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