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Swedish Mathematical Competition
2001 Swedish Mathematical Competition
4
4
Part of
2001 Swedish Mathematical Competition
Problems
(1)
<ABC wanted, EF bisects <AFD and <ADC = 80^o, circle
Source: 2001 Swedish Mathematical Competition p4
3/21/2021
A
B
C
ABC
A
BC
is a triangle. A circle through
A
A
A
touches the side
B
C
BC
BC
at
D
D
D
and intersects the sides
A
B
AB
A
B
and
A
C
AC
A
C
again at
E
,
F
E, F
E
,
F
respectively.
E
F
EF
EF
bisects
∠
A
F
D
\angle AFD
∠
A
F
D
and
∠
A
D
C
=
8
0
o
\angle ADC = 80^o
∠
A
D
C
=
8
0
o
. Find
∠
A
B
C
\angle ABC
∠
A
BC
.
geometry
angles