MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
5
Triangle and points
Triangle and points
Source: St Petersburg Olympiad 2018, Grade 9, P5
July 13, 2018
geometry
Problem Statement
Can we draw
△
A
B
C
\triangle ABC
△
A
BC
and points
X
,
Y
X,Y
X
,
Y
, such that
A
X
=
B
Y
=
A
B
AX=BY=AB
A
X
=
B
Y
=
A
B
,
B
X
=
C
Y
=
B
C
BX = CY = BC
BX
=
C
Y
=
BC
,
C
X
=
A
Y
=
C
A
CX = AY = CA
CX
=
A
Y
=
C
A
?
Back to Problems
View on AoPS