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Baltic Way
2023 Baltic Way
13
13
Part of
2023 Baltic Way
Problems
(1)
Conditional geo with angle equality
Source: Baltic Way 2023/13
11/11/2023
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
and incenter
I
I
I
. Let
D
D
D
be the projection of
I
I
I
onto
B
C
BC
BC
. Let
H
H
H
be the orthocenter of
A
B
C
ABC
A
BC
and suppose that
∠
I
D
H
=
∠
C
B
A
−
∠
A
C
B
\angle IDH=\angle CBA-\angle ACB
∠
I
DH
=
∠
CB
A
−
∠
A
CB
. Prove that
A
H
=
2
I
D
AH=2ID
A
H
=
2
I
D
.
geometry