MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2022 Latvia Baltic Way TST
P12
P12
Part of
2022 Latvia Baltic Way TST
Problems
(1)
Incentre configuration with parallel lines desired
Source: Latvian TST for Baltic Way 2022 P12
11/25/2022
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with incentre
I
I
I
. Points
E
E
E
and
F
F
F
are the tangency points of the incircle and the sides
A
C
AC
A
C
and
A
B
AB
A
B
, respectively. Suppose that the lines
B
I
BI
B
I
and
C
I
CI
C
I
intersect the line
E
F
EF
EF
at
Y
Y
Y
and
Z
Z
Z
, respectively. Let
M
M
M
denote the midpoint of the segment
B
C
BC
BC
, and
N
N
N
denote the midpoint of the segment
Y
Z
YZ
Y
Z
. Prove that
A
I
∥
M
N
AI \parallel MN
A
I
∥
MN
.
geometry
incenter