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Saint Petersburg Mathematical Olympiad
2022 Saint Petersburg Mathematical Olympiad
2
Conditional geo with angle 45°
Conditional geo with angle 45°
Source: St Petersburg 2022 11.2
September 28, 2022
geometry
Problem Statement
Given is a triangle
A
B
C
ABC
A
BC
with
∠
B
A
C
=
45
\angle BAC=45
∠
B
A
C
=
45
;
A
D
,
B
E
,
C
F
AD, BE, CF
A
D
,
BE
,
CF
are altitudes and
E
F
∩
B
C
=
X
EF \cap BC=X
EF
∩
BC
=
X
. If
A
X
∥
D
E
AX \parallel DE
A
X
∥
D
E
, find the angles of the triangle.
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