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Chile National Olympiad
2022 Chile National Olympiad
2
2
Part of
2022 Chile National Olympiad
Problems
(1)
ID =IE if <ACB=60^o, 2 angle bisectors and incenter
Source: 2022 Chile National Olympiad level 2 p2
10/22/2022
Let
A
B
C
ABC
A
BC
be a triangle such that
∠
C
A
B
=
6
0
o
\angle CAB = 60^o
∠
C
A
B
=
6
0
o
. Consider
D
,
E
D, E
D
,
E
points on sides
A
C
AC
A
C
and
A
B
AB
A
B
respectively such that
B
D
BD
B
D
bisects angle
∠
A
B
C
\angle ABC
∠
A
BC
,
C
E
CE
CE
bisects angle
∠
B
C
A
\angle BCA
∠
BC
A
and let
I
I
I
be the intersection of them. Prove that
∣
I
D
∣
=
∣
I
E
∣
|ID| =|IE|
∣
I
D
∣
=
∣
I
E
∣
.
equal segments
geometry
incenter