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2013 HMIC
3
3
Part of
2013 HMIC
Problems
(1)
2013 HMIC p3 geometry
Source:
9/20/2019
Triangle
A
B
C
ABC
A
BC
is inscribed in a circle
ω
\omega
ω
such that
∠
A
=
6
0
o
\angle A = 60^o
∠
A
=
6
0
o
and
∠
B
=
7
5
o
\angle B = 75^o
∠
B
=
7
5
o
. Let the bisector of angle
A
A
A
meet
B
C
BC
BC
and
ω
\omega
ω
at
E
E
E
and
D
D
D
, respectively. Let the reflections of
A
A
A
across
D
D
D
and
C
C
C
be
D
′
D'
D
′
and
C
′
C'
C
′
, respectively. If the tangent to
ω
\omega
ω
at
A
A
A
meets line
B
C
BC
BC
at
P
P
P
, and the circumcircle of
A
P
D
′
APD'
A
P
D
′
meets line
A
C
AC
A
C
at
F
≠
A
F \ne A
F
=
A
, prove that the circumcircle of
C
′
F
E
C'FE
C
′
FE
is tangent to
B
C
BC
BC
at
E
E
E
.
circumcircle
geometry