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National and Regional Contests
Serbia Contests
Serbia National Math Olympiad
2016 Serbia National Math Olympiad
4
4
Part of
2016 Serbia National Math Olympiad
Problems
(1)
Easy geometry
Source: Serbia Math Olympiad 2016
4/2/2016
Let
A
B
C
ABC
A
BC
be a triangle, and
I
I
I
the incenter,
M
M
M
midpoint of
B
C
BC
BC
,
D
D
D
the touch point of incircle and
B
C
BC
BC
. Prove that perpendiculars from
M
,
D
,
A
M, D, A
M
,
D
,
A
to
A
I
,
I
M
,
B
C
AI, IM, BC
A
I
,
I
M
,
BC
respectively are concurrent
geometry
incenter