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National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2023 Czech and Slovak Olympiad III A.
3
3
Part of
2023 Czech and Slovak Olympiad III A.
Problems
(1)
SKMO 2023 P3
Source:
4/4/2023
In acute triangle
A
B
C
ABC
A
BC
let
H
H
H
be its orthocenter and
I
I
I
be its incenter. Let
D
D
D
be the projection of point
I
I
I
onto the line
B
C
BC
BC
and
E
E
E
be the reflection of point
A
A
A
in point
I
I
I
. Further, let
F
F
F
be the projection of point
H
H
H
onto the line
E
D
ED
E
D
. Prove that points
B
,
H
,
F
B, H, F
B
,
H
,
F
and
C
C
C
lie on circle.
geometry