MathDB
Problems
Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2013 Bangladesh Mathematical Olympiad
8
8
Part of
2013 Bangladesh Mathematical Olympiad
Problems
(1)
Find the angle.
Source:
8/18/2016
△
A
B
C
\triangle ABC
△
A
BC
is an acute angled triangle. Perpendiculars drawn from its vertices on the opposite sides are
A
D
AD
A
D
,
B
E
BE
BE
and
C
F
CF
CF
. The line parallel to
D
F
DF
D
F
through
E
E
E
meets
B
C
BC
BC
at
Y
Y
Y
and
B
A
BA
B
A
at
X
X
X
.
D
F
DF
D
F
and
C
A
CA
C
A
meet at
Z
Z
Z
. Circumcircle of
X
Y
Z
XYZ
X
Y
Z
meets
A
C
AC
A
C
at
S
S
S
. Given,
∠
B
=
3
3
∘
.
\angle B=33 ^\circ.
∠
B
=
3
3
∘
.
find the angle
∠
F
S
D
\angle FSD
∠
FS
D
with proof.
geometry