MathDB
Problems
Contests
International Contests
Baltic Way
2023 Baltic Way
12
12
Part of
2023 Baltic Way
Problems
(1)
Incenter of a weird triangle
Source: Baltic Way 2023/12
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
. The internal angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
meets
B
C
BC
BC
at
D
D
D
. Let
O
O
O
be the circumcenter of
A
B
C
ABC
A
BC
and let
A
O
AO
A
O
meet
B
C
BC
BC
at
E
E
E
. Let
J
J
J
be the incenter of triangle
A
E
D
AED
A
E
D
. Show that if
∠
A
D
O
=
4
5
∘
\angle ADO=45^{\circ}
∠
A
D
O
=
4
5
∘
, then
O
J
=
J
D
OJ=JD
O
J
=
J
D
.
geometry