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International Contests
EGMO
2019 EGMO
3
3
Part of
2019 EGMO
Problems
(1)
Concurrent angle bisectors
Source: EGMO 2019 Problem 3
4/9/2019
Let
A
B
C
ABC
A
BC
be a triangle such that
∠
C
A
B
>
∠
A
B
C
\angle CAB > \angle ABC
∠
C
A
B
>
∠
A
BC
, and let
I
I
I
be its incentre. Let
D
D
D
be the point on segment
B
C
BC
BC
such that
∠
C
A
D
=
∠
A
B
C
\angle CAD = \angle ABC
∠
C
A
D
=
∠
A
BC
. Let
ω
\omega
ω
be the circle tangent to
A
C
AC
A
C
at
A
A
A
and passing through
I
I
I
. Let
X
X
X
be the second point of intersection of
ω
\omega
ω
and the circumcircle of
A
B
C
ABC
A
BC
. Prove that the angle bisectors of
∠
D
A
B
\angle DAB
∠
D
A
B
and
∠
C
X
B
\angle CXB
∠
CXB
intersect at a point on line
B
C
BC
BC
.
geometry
EGMO 2019