Construct a circle

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Circles a and b intersect at M and N. Construct a circle k orthogonal to Circles a and b and touching third given circle c.

Problem is supposed to be solved using inversion and/or power of a point.

Since a and b intersect at M and N and k is supposed to be orthogonal to them we can conclude that center of k belongs to radical axis of a and b which is a line through M and N.

If the radical axis goes through center of a circle c I think that problem then becomes : construct a circle orthogonal to two given Circles which contains a given point (which I know how to construct)

But what happens if this isn't the case?

I hope this makes sense (English isn't my native).

Any hints would be appreciated.