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Two circles

Source: 64 Polish MO 2013 Second Round - Problem 2

April 21, 2018
geometrycirclesincirclePolandincenter

Problem Statement

Circles o1o_1 and o2o_2 with centers in O1O_1 and O2O_2, respectively, intersect in two different points AA and BB, wherein angle O1AO2O_1AO_2 is obtuse. Line O1BO_1B intersects circle o2o_2 in point C≠BC \neq B. Line O2BO_2B intersects circle o1o_1 in point D≠BD \neq B. Show that point BB is incenter of triangle ACDACD.
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