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Nordic
2008 Nordic
3
Nordic MC 2008 Q3
Nordic MC 2008 Q3
Source:
March 3, 2013
geometry
circumcircle
geometry unsolved
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle and
D
,
E
D,E
D
,
E
be points on
B
C
,
C
A
BC,CA
BC
,
C
A
such that
A
D
,
B
E
AD,BE
A
D
,
BE
are angle bisectors of
△
A
B
C
\triangle ABC
△
A
BC
. Let
F
,
G
F,G
F
,
G
be points on the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
such that
A
F
∣
∣
D
E
AF||DE
A
F
∣∣
D
E
and
F
G
∣
∣
B
C
FG||BC
FG
∣∣
BC
. Prove that
A
G
B
G
=
A
B
+
A
C
A
B
+
B
C
\frac{AG}{BG}= \frac{AB+AC}{AB+BC}
BG
A
G
=
A
B
+
BC
A
B
+
A
C
.
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