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PQ _|_ RS , 2 centroids, 2 orthocenters 2015-16 Dürer Round1 D+3

Source:

December 5, 2022

geometryperpendicularDurer

Problem Statement

Let

M

be the intersection point of the diagonals of the convex quadrilateral

ABCD

. Let

P

and

Q

be the centroids of triangles

AMD

and

BMC

respectively. Let

R

and

S

are the orthocenters of triangles

AMB

and

CMD

. Prove that the lines

P Q

and

RS

are perpendicular to each other.