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Some geometry

Source: St Petersburg Olympiad 2014, Grade 9, P2

October 27, 2017
geometrycircumcircleangle bisector

Problem Statement

All angles of ABCABC are in (30,90)(30,90). Circumcenter of ABCABC is OO and circumradius is RR. Point KK is projection of OO to angle bisector of ∠B\angle B, point MM is midpoint ACAC. It is known, that 2KM=R2KM=R. Find ∠B\angle B
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