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Baltic Way
2018 Baltic Way
12
12
Part of
2018 Baltic Way
Problems
(1)
Geometry with right angles and length conditions
Source: Baltic Way 2018, Problem 12
11/6/2018
The altitudes
B
B
1
BB_1
B
B
1
and
C
C
1
CC_1
C
C
1
of an acute triangle
A
B
C
ABC
A
BC
intersect in point
H
H
H
. Let
B
2
B_2
B
2
and
C
2
C_2
C
2
be points on the segments
B
H
BH
B
H
and
C
H
CH
C
H
, respectively, such that
B
B
2
=
B
1
H
BB_2=B_1H
B
B
2
=
B
1
H
and
C
C
2
=
C
1
H
CC_2=C_1H
C
C
2
=
C
1
H
. The circumcircle of the triangle
B
2
H
C
2
B_2HC_2
B
2
H
C
2
intersects the circumcircle of the triangle
A
B
C
ABC
A
BC
in points
D
D
D
and
E
E
E
. Prove that the triangle
D
E
H
DEH
D
E
H
is right-angled.
geometry