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Problems
Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
3
3
Part of
2019 Bangladesh Mathematical Olympiad
Problems
(1)
BdMO National Higher Secondary 2019/3
Source: BdMO National Higher Secondary 2019/3
3/4/2019
Let
α
\alpha
α
and
ω
\omega
ω
be two circles such that
ω
\omega
ω
goes through the center of
α
\alpha
α
.
ω
\omega
ω
intersects
α
\alpha
α
at
A
A
A
and
B
B
B
.Let
P
P
P
any point on the circumference
ω
\omega
ω
.The lines
P
A
PA
P
A
and
P
B
PB
PB
intersects
α
\alpha
α
again at
E
E
E
and
F
F
F
respectively.Prove that
A
B
=
E
F
AB=EF
A
B
=
EF
.
geometry