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2003 JBMO Shortlist
5
5
Part of
2003 JBMO Shortlist
Problems
(1)
semicircle tangent to isosceles triangle
Source: JBMO Shortlist 2003
10/12/2017
Let
A
B
C
ABC
A
BC
be an isosceles triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
. A semi-circle of diameter
[
E
F
]
[EF]
[
EF
]
with
E
,
F
ā
[
B
C
]
E, F \in [BC]
E
,
F
ā
[
BC
]
, is tangent to the sides
A
B
,
A
C
AB,AC
A
B
,
A
C
in
M
,
N
M, N
M
,
N
respectively and
A
E
AE
A
E
intersects the semicircle at
P
P
P
. Prove that
P
F
PF
PF
passes through the midpoint of
[
M
N
]
[MN]
[
MN
]
.
geometry
JBMO