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Part of 1992 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

equal radii of circumcircles

Source: 2nd Rioplatense Olympiad 1992 level 3 P3

9/4/2018
Let DD be the center of the circumcircle of the acute triangle ABCABC. If the circumcircle of triangle ADBADB intersects ACAC (or its extension) at MM and also BCBC (or its extension) at NN, show that the radii of the circumcircles of △ADB\triangle ADB and △MNC\triangle MNC are equal.
geometrycircumradiuscircumcircle