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.