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IMO Shortlist
2014 IMO Shortlist
G2
G2
Part of
2014 IMO Shortlist
Problems
(1)
IMO Shortlist 2014 G2
Source:
7/11/2015
Let
A
B
C
ABC
A
BC
be a triangle. The points
K
,
L
,
K, L,
K
,
L
,
and
M
M
M
lie on the segments
B
C
,
C
A
,
BC, CA,
BC
,
C
A
,
and
A
B
,
AB,
A
B
,
respectively, such that the lines
A
K
,
B
L
,
AK, BL,
A
K
,
B
L
,
and
C
M
CM
CM
intersect in a common point. Prove that it is possible to choose two of the triangles
A
L
M
,
B
M
K
,
ALM, BMK,
A
L
M
,
BM
K
,
and
C
K
L
CKL
C
K
L
whose inradii sum up to at least the inradius of the triangle
A
B
C
ABC
A
BC
.Proposed by Estonia
IMO Shortlist
geometry