MathDB

4

Part of 1991 Mexico National Olympiad

Problems(1)

8 points concyclic

Source: Mexican Mathematical Olympiad 1991 OMM P4

7/29/2018
The diagonals ACAC and BDBD of a convex quarilateral ABCDABCD are orthogonal. Let M,N,R,SM,N,R,S be the midpoints of the sides AB,BC,CDAB,BC,CD and DADA respectively, and let W,X,Y,ZW,X,Y,Z be the projections of the points M,N,RM,N,R and SS on the lines CD,DA,ABCD,DA,AB and BCBC, respectively. Prove that the points M,N,R,S,W,X,YM,N,R,S,W,X,Y and ZZ lie on a circle.
geometryorthogonalconvex quadrilateralConcyclic