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cyclic ABCD with <ABD <DBC given, cyclic from 2 midpoints wanted

Source:

August 4, 2019
geometrycyclic quadrilateralequal anglesmidpoint

Problem Statement

Let ABCDABCD be a cyclic quadrilateral satisfying ∠ABD=∠DBC\angle ABD = \angle DBC. Let EE be the intersection of the diagonals ACAC and BDBD. Let MM be the midpoint of AEAE, and NN be the midpoint of DCDC. Show that MBCNMBCN is a cyclic quadrilateral.
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