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Indonesia Regional MO OSP SMA - geometry
2008.3
2008.3
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
Triangle
Source: Indonesia 2nd Round 2008
6/25/2008
Given triangle
A
B
C
ABC
A
BC
. The incircle of triangle
A
B
C
ABC
A
BC
is tangent to
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
at
D
,
E
,
F
D,E,F
D
,
E
,
F
respectively. Construct point
G
G
G
on
E
F
EF
EF
such that
D
G
DG
D
G
is perpendicular to
E
F
EF
EF
. Prove that \frac{FG}{EG} \equal{} \frac{BF}{CE}.
geometry
trigonometry
geometry unsolved