Transform by inversion of the circumcircle

Consider the inversion of pole I , the incenter of a triangle ABC , with leaves invariant the incircle of ABC. Let D,E,F the tangent points of the incircle to the sides of ABC.
Circles of diameter IE,ID,IF intersect in K,L,M. Then circle by K,L,M is the transform by inversion of the circumcircle of triangle ABC.


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