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Math Prize For Girls Problems
2012 Math Prize For Girls Problems
10
10
Part of
2012 Math Prize For Girls Problems
Problems
(1)
Math Prize 2012 Problem 10
Source:
9/24/2012
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with a right angle
∠
A
B
C
\angle ABC
∠
A
BC
. Let
D
D
D
be the midpoint of
B
C
‾
\overline{BC}
BC
, let
E
E
E
be the midpoint of
A
C
‾
\overline{AC}
A
C
, and let
F
F
F
be the midpoint of
A
B
‾
\overline{AB}
A
B
. Let
G
G
G
be the midpoint of
E
C
‾
\overline{EC}
EC
. One of the angles of
△
D
F
G
\triangle DFG
△
D
FG
is a right angle. What is the least possible value of
B
C
A
G
\frac{BC}{AG}
A
G
BC
?