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Prove that SB'M and SA'N are similar - ISL 1978

Source:

September 20, 2010

symmetrygeometrysimilar trianglesEquilateral TriangleIMO Shortlist

Problem Statement

Two identically oriented equilateral triangles,

ABC

with center

S

and

A'B'C

, are given in the plane. We also have

A' \neq S

and

B' \neq S

. If

M

is the midpoint of

A'B

and

N

the midpoint of

AB'

, prove that the triangles

SB'M

and

SA'N

are similar.