MathDB
Problems
Contests
National and Regional Contests
Austria Contests
Austrian MO National Competition
1991 Federal Competition For Advanced Students
4
4
Part of
1991 Federal Competition For Advanced Students
Problems
(1)
circle
Source: Austria 1991
7/10/2009
Let
A
B
AB
A
B
be a chord of a circle
k
k
k
of radius
r
r
r
, with AB\equal{}c.
(
a
)
(a)
(
a
)
Construct the triangle
A
B
C
ABC
A
BC
with
C
C
C
on
k
k
k
in which a median from
A
A
A
or
B
B
B
is of a given length
d
.
d.
d
.
(
b
)
(b)
(
b
)
For which
c
c
c
and
d
d
d
is this triangle unique?
geometry proposed
geometry