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National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
7
7
Part of
2019 Bangladesh Mathematical Olympiad
Problems
(1)
BdMO National Higher Secondary 2019/7
Source: BdMO National Higher Secondary 2019/7
3/4/2019
Given three cocentric circles
ω
1
\omega_1
ω
1
,
ω
2
\omega_2
ω
2
,
ω
3
\omega_3
ω
3
with radius
r
1
,
r
2
,
r
3
r_1,r_2,r_3
r
1
,
r
2
,
r
3
such that
r
1
+
r
3
≥
2
r
2
r_1+r_3\geq {2r_2}
r
1
+
r
3
≥
2
r
2
.Constrat a line that intersects
ω
1
\omega_1
ω
1
,
ω
2
\omega_2
ω
2
,
ω
3
\omega_3
ω
3
at
A
,
B
,
C
A,B,C
A
,
B
,
C
respectively such that
A
B
=
B
C
AB=BC
A
B
=
BC
.
geometry