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Problems
Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2013 Bangladesh Mathematical Olympiad
9
9
Part of
2013 Bangladesh Mathematical Olympiad
Problems
(1)
Find the angle!
Source:
2/9/2017
Six points
A
,
B
,
C
,
D
,
E
,
F
A, B, C, D, E, F
A
,
B
,
C
,
D
,
E
,
F
are chosen on a circle anticlockwise. None of
A
B
,
C
D
,
E
F
AB, CD, EF
A
B
,
C
D
,
EF
is a diameter. Extended
A
B
AB
A
B
and
D
C
DC
D
C
meet at
Z
,
C
D
Z, CD
Z
,
C
D
and
F
E
FE
FE
at
X
,
E
F
X, EF
X
,
EF
and
B
A
BA
B
A
at
Y
.
A
C
Y. AC
Y
.
A
C
and
B
F
BF
BF
meets at
P
,
C
E
P, CE
P
,
CE
and
B
D
BD
B
D
at
Q
Q
Q
and
A
E
AE
A
E
and
D
F
DF
D
F
at
R
.
R.
R
.
If
O
O
O
is the point of intersection of
Y
Q
YQ
Y
Q
and
Z
R
,
ZR,
ZR
,
find the
∠
X
O
P
.
\angle XOP.
∠
XOP
.
geometry
angle
circles