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Problems
Contests
National and Regional Contests
Korea Contests
Korea Winter Program Practice Test
2020 Korean MO winter camp
#4
#4
Part of
2020 Korean MO winter camp
Problems
(1)
Line DT tangent to incircle
Source: 2020 Korean MO winter camp Test 1 P4
9/7/2020
I
I
I
is the incenter of a given triangle
△
A
B
C
\triangle ABC
△
A
BC
. The angle bisectors of
A
B
C
ABC
A
BC
meet the sides at
D
,
E
,
F
D,E,F
D
,
E
,
F
, and
E
F
EF
EF
meets
(
A
B
C
)
(ABC)
(
A
BC
)
at
L
L
L
and
T
T
T
(
F
F
F
is on segment
L
E
LE
L
E
.). Suppose
M
M
M
is the midpoint of
B
C
BC
BC
. Prove that if
D
T
DT
D
T
is tangent to the incircle of
A
B
C
ABC
A
BC
, then
I
L
IL
I
L
bisects
∠
M
L
T
\angle MLT
∠
M
L
T
.
geometry