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midpoint wanted, angle bisectors related, <BCD = <ADC >= 90 ^o

Source: 2011 Romanian NMO grade VII P3

May 18, 2020
geometryangle bisectormidpointequal angles

Problem Statement

In the convex quadrilateral ABCDABCD we have that ∠BCD=∠ADC≥90o\angle BCD = \angle ADC \ge 90 ^o. The bisectors of ∠BAD\angle BAD and ∠ABC\angle ABC intersect in MM. Prove that if M∈CDM \in CD, then MM is the middle of CDCD.
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