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Easy 3d geometry from All-Russian olympiad

Source: All-Russian 2021/11.6

April 20, 2021

geometry3D geometrytetrahedronperpendicular bisector

Problem Statement

In tetrahedron

ABCS

no two edges have equal length. Point

A'

in plane

BCS

is symmetric to

S

with respect to the perpendicular bisector of

BC

. Points

B'

and

C'

are defined analagously. Prove that planes

ABC, AB'C', A'BC'

abd

A'B'C

share a common point.