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2018 Kürschák Competition
1
1
Part of
2018 Kürschák Competition
Problems
(1)
Seem like some well-known lemma
Source: Kürchák 2018 P1
10/8/2018
Given a triangle
A
B
C
ABC
A
BC
with its incircle touching sides
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
at
A
1
,
B
1
,
C
1
A_1,B_1,C_1
A
1
,
B
1
,
C
1
, respectively. Let the median from
A
A
A
intersects
B
1
C
1
B_1C_1
B
1
C
1
at
M
M
M
. Show that
A
1
M
⊥
B
C
A_1M\perp BC
A
1
M
⊥
BC
.
geometry