MathDB

1

Part of 2017 EGMO

Problems(1)

Cyclic Points

Source: EGMO 2017 Day1 P1

4/8/2017
Let ABCDABCD be a convex quadrilateral with ∠DAB=∠BCD=90∘\angle DAB=\angle BCD=90^{\circ} and ∠ABC>∠CDA\angle ABC> \angle CDA. Let QQ and RR be points on segments BCBC and CDCD, respectively, such that line QRQR intersects lines ABAB and ADAD at points PP and SS, respectively. It is given that PQ=RSPQ=RS.Let the midpoint of BDBD be MM and the midpoint of QRQR be NN.Prove that the points M,N,AM,N,A and CC lie on a circle.
cylicgeometryAngle ChasingquadrilateralEGMOEGMO 2017barycentric coordinates