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AMC 12/AHSME
1984 AMC 12/AHSME
27
Triangles, triangles, triangles
Triangles, triangles, triangles
Source:
October 24, 2005
geometry
perpendicular bisector
similar triangles
Problem Statement
In
△
A
B
C
\triangle ABC
△
A
BC
,
D
D
D
is on
A
C
AC
A
C
and
F
F
F
is on
B
C
BC
BC
. Also,
A
B
⊥
A
C
,
A
F
⊥
B
C
AB \perp AC, AF \perp BC
A
B
⊥
A
C
,
A
F
⊥
BC
, and
B
D
=
D
C
=
F
C
=
1
BD = DC = FC = 1
B
D
=
D
C
=
FC
=
1
. Find
A
C
AC
A
C
. A.
2
\sqrt{2}
2
B.
3
\sqrt{3}
3
C.
2
3
\sqrt[3] {2}
3
2
D.
3
3
\sqrt[3] {3}
3
3
E.
3
4
\sqrt[4] {3}
4
3
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