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Thailand Online MO
2023 Thailand Online MO
8
8
Part of
2023 Thailand Online MO
Problems
(1)
Prove that B is the incenter of DEC’
Source: 2023 Thailand Online MO P8
2/12/2023
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
. Let
M
M
M
be the midpoint of
B
C
BC
BC
and
E
E
E
be the foot of altitude from
B
B
B
to
A
C
AC
A
C
. The point
C
′
C'
C
′
is the reflection of
C
C
C
across
A
M
AM
A
M
. The point
D
D
D
not equal to
C
C
C
is placed on line
B
C
BC
BC
such that
A
D
=
A
C
AD=AC
A
D
=
A
C
. Prove that
B
B
B
is the incenter of triangle
D
E
C
′
DEC'
D
E
C
′
.
geometry