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Lusophon Mathematical Olympiad
2021 Lusophon Mathematical Olympiad
3
3
Part of
2021 Lusophon Mathematical Olympiad
Problems
(1)
A line tangent to a circumcircle
Source: Lusophon Mathematical Olympiad 2021 Problem 3
12/19/2021
Let triangle
A
B
C
ABC
A
BC
be an acute triangle with
A
B
≠
A
C
AB\neq AC
A
B
=
A
C
. The bisector of
B
C
BC
BC
intersects the lines
A
B
AB
A
B
and
A
C
AC
A
C
at points
F
F
F
and
E
E
E
, respectively. The circumcircle of triangle
A
E
F
AEF
A
EF
has center
P
P
P
and intersects the circumcircle of triangle
A
B
C
ABC
A
BC
at point
D
D
D
with
D
D
D
different to
A
A
A
.Prove that the line
P
D
PD
P
D
is tangent to the circumcircle of triangle
A
B
C
ABC
A
BC
.
geometry
circumcircle