MathDB
BM = DN wanted , ABCD rectangle, QB = QC, RC = RD, 2 circles

Source: 2021 Saudi Arabia Training Lists p5 / 2016 Vietnam IMO Training

January 4, 2022
geometryrectangleequal segments

Problem Statement

Let ABCDABCD be a rectangle with PP lies on the segment ACAC. Denote QQ as a point on minor arc PBPB of (PAB)(PAB) such that QB=QCQB = QC. Denote RR as a point on minor arc PDPD of (PAD)(PAD) such that RC=RDRC = RD. The lines CBCB, CDCD meet (CQR)(CQR) again at M,NM, N respectively. Prove that BM=DNBM = DN.
by Tran Quang Hung
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