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8 points concyclic

Source: Mexican Mathematical Olympiad 1991 OMM P4

July 29, 2018

geometryorthogonalconvex quadrilateralConcyclic

Problem Statement

The diagonals

AC

and

BD

of a convex quarilateral

ABCD

are orthogonal. Let

M,N,R,S

be the midpoints of the sides

AB,BC,CD

and

DA

respectively, and let

W,X,Y,Z

be the projections of the points

M,N,R

and

S

on the lines

CD,DA,AB

and

BC

, respectively. Prove that the points

M,N,R,S,W,X,Y

and

Z

lie on a circle.

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