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Putnam
1958 February Putnam
B1
B1
Part of
1958 February Putnam
Problems
(1)
Putnam 1958 February B1
Source: Putnam 1958 February
7/18/2022
i) Given line segments
A
,
B
,
C
,
D
A,B,C,D
A
,
B
,
C
,
D
with
A
A
A
the longest, construct a quadrilateral with these sides and with
A
A
A
and
B
B
B
parallel, when possible. ii) Given any acute-angled triangle
A
B
C
ABC
A
BC
and one altitude
A
H
AH
A
H
, select any point
D
D
D
on
A
H
AH
A
H
, then draw
B
D
BD
B
D
and extend until it intersects
A
C
AC
A
C
in
E
E
E
, and draw
C
D
CD
C
D
and extend until it intersects
A
B
AB
A
B
in
F
F
F
. Prove that
∠
A
H
E
=
∠
A
H
F
\angle AHE = \angle AHF
∠
A
H
E
=
∠
A
H
F
.
Putnam
geometry
Triangles