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Bosnia and Herzegovina 2022 BMO TST P3

Source:

May 22, 2022
geometrycyclic quadrilateralangle bisectorcircumcircle

Problem Statement

Cyclic quadrilateral ABCDABCD is inscribed in circle kk with center OO. The angle bisector of ABDABD intersects ADAD and kk in K,MK,M respectively, and the angle bisector of CBDCBD intersects CDCD and kk in L,NL,N respectively. If KL∥MNKL\parallel MN prove that the circumcircle of triangle MONMON bisects segment BDBD.
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