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collinear in 3D wanted, cube related, perpendicular on plane

Source: 2008 Romania District VIII P3, Gazeta Matematica, 2007

May 18, 2020

geometry3D geometrycollinearperpendicularSymmetric

Problem Statement

Let

ABCDA' B' C' D '

be a cube ,

M

the foot of the perpendicular from

A

on the plane

(A'CD)

N

the foot of the perpendicular from

B

on the diagonal

A'C

and

P

is symmetric of the point

D

with respect to

C

. Show that the points

M, N, P

are collinear.