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KoMaL A Problems
KoMaL A Problems 2022/2023
A. 855
A. 855
Part of
KoMaL A Problems 2022/2023
Problems
(1)
IO lines in two triangles intersect on circumcircle
Source: KoMaL A. 855
6/13/2023
In scalene triangle
A
B
C
ABC
A
BC
the shortest side is
B
C
BC
BC
. Let points
M
M
M
and
N
N
N
be chosen on sides
A
B
AB
A
B
and
A
C
AC
A
C
, respectively, such that
B
M
=
C
N
=
B
C
BM=CN=BC
BM
=
CN
=
BC
. Let
I
I
I
and
O
O
O
denote the incenter and circumcentre of triangle
A
B
C
ABC
A
BC
, and let
D
D
D
and
E
E
E
denote the incenter and circumcenter of triangle
A
M
N
AMN
A
MN
. Prove that lines
I
O
IO
I
O
and
D
E
DE
D
E
intersect each other on the circumcircle of triangle
A
B
C
ABC
A
BC
.Submitted by Luu Dong, Vietnam
geometry
circumcircle