MathDB

Romania NMO 2023 Grade 8 P4

Source: Romania National Olympiad 2023

April 14, 2023

3D geometrygeometrytetrahedron

Problem Statement

Let

ABCD

be a tetrahedron and

M

and

N

be the midpoints of

AC

and

BD

, respectively. Show that for every point

P \in (MN)

with

P \neq M

and

P \neq N

, there exist unique points

X

and

Y

on segments

AB

and

CD

, respectively, such that

X,P,Y

are collinear.

Back to Problems View on AoPS