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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
8.5
8.5
Part of
1997 All-Russian Olympiad Regional Round
Problems
(1)
triangle coveved by 3 squares - All-Russian MO 1997 Regional (R4) 8.5
Source:
9/23/2024
Segments
A
B
AB
A
B
,
B
C
BC
BC
and
C
A
CA
C
A
are, respectively, diagonals of squares
K
1
K_1
K
1
,
K
2
K_2
K
2
,
K
3
K3
K
3
. Prove that if triangle
A
B
C
ABC
A
BC
is acute, then it completely covered by squares
K
1
K_1
K
1
,
K
2
K_2
K
2
and
K
3
K_3
K
3
.
geometry
Squares
geometric inequality