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Contests
National and Regional Contests
Italy Contests
ITAMO
2020 ITAMO
4
4
Part of
2020 ITAMO
Problems
(1)
Isosceles and Concurrency
Source: Italy National Olympiad 2020 P4
9/30/2020
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with
A
B
=
A
C
AB=AC
A
B
=
A
C
, let
D
D
D
be the foot of perpendicular, of the point
C
C
C
, to the line
A
B
AB
A
B
and the point
M
M
M
is the midpoint of
A
C
AC
A
C
. Finally, the point
E
E
E
is the second intersection of the line
B
C
BC
BC
and the circumcircle of
△
C
D
M
\triangle CDM
△
C
D
M
. Prove that the lines
A
E
,
B
M
AE, BM
A
E
,
BM
and
C
D
CD
C
D
are concurrents if and only if
C
E
=
C
M
CE=CM
CE
=
CM
.
geometry
circumcircle