IMO 1993 SL 3

Consider the triangle ABC, its circumcircle k with center O

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IMO 1993 SL 3

Origin: SPA

Problem

Consider the triangle ABC, its circumcircle k with center O and radius R, and its incircle with center I and radius r. Another circle kc is tangent to the sides CA, CB at D, E, respectively, and it is internally tangent to k. Show that the incenter I is the midpoint of DE.