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Some another geometry

Source: Tuymaada 2015, Day 2, Problem 7, Senior League

July 10, 2017
geometrycircumcircle

Problem Statement

In △ABC\triangle ABC points M,OM,O are midpoint of ABAB and circumcenter. It is true, that OM=R−rOM=R-r. Bisector of external ∠A\angle A intersect BCBC at DD and bisector of external ∠C\angle C intersect ABAB at EE. Find possible values of ∠CED\angle CED
D. Shiryaev
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