MathDB
Problems
Contests
National and Regional Contests
Azerbaijan Contests
JBMO TST - Azerbaijan
2017 Azerbaijan JBMO TST
3
Romania JBMO TST 2016 4
Romania JBMO TST 2016 4
Source:
April 25, 2016
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
and
D
,
E
,
F
D,E,F
D
,
E
,
F
be the contact points of the incircle
(
I
)
(I)
(
I
)
with
B
C
,
A
C
,
A
B
BC,AC,AB
BC
,
A
C
,
A
B
. Let
M
,
N
M,N
M
,
N
be on
E
F
EF
EF
such that
M
B
⊥
B
C
MB \perp BC
MB
⊥
BC
and
N
C
⊥
B
C
NC \perp BC
NC
⊥
BC
.
M
D
MD
M
D
and
N
D
ND
N
D
intersect the
(
I
)
(I)
(
I
)
in
D
D
D
and
Q
Q
Q
. Prove that
D
P
=
D
Q
DP=DQ
D
P
=
D
Q
.
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