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Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
9.6
9.6
Part of
VII Soros Olympiad 2000 - 01
Problems
(1)
ratio wanted, rectangle inscribed in triangle (VII Soros Olympiad R1 9.6)
Source:
7/4/2021
Two vertices of the rectangle are located on side
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
, and the other two are on sides
A
B
AB
A
B
and
A
C
AC
A
C
. It is known that the midpoint of the altitude of this triangle, drawn on the side
B
C
BC
BC
, lies on one of the diagonals of the rectangle, and the side of the rectangle located on
B
C
BC
BC
is three times less than
B
C
BC
BC
. In what ratio does the altitude of the triangle divide the side
B
C
BC
BC
?
ratio
geometry
rectangle