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Bangladesh Contests
Bangladesh Mathematical Olympiad
2015 Bangladesh Mathematical Olympiad
6
6
Part of
2015 Bangladesh Mathematical Olympiad
Problems
(1)
Weird Trapezium problem
Source: Bangladesh National Mathematical Olympiad 2015
2/25/2019
Trapezoid
A
B
C
D
ABCD
A
BC
D
has sides
A
B
=
92
,
B
C
=
50
,
C
D
=
19
,
A
D
=
70
AB=92,BC=50,CD=19,AD=70
A
B
=
92
,
BC
=
50
,
C
D
=
19
,
A
D
=
70
A
B
AB
A
B
is parallel to
C
D
CD
C
D
A circle with center
P
P
P
on
A
B
AB
A
B
is drawn tangent to
B
C
BC
BC
and
A
D
AD
A
D
.Given that
A
P
=
m
n
AP=\dfrac mn
A
P
=
n
m
(Where
m
,
n
m,n
m
,
n
are relatively prime).What is
m
+
n
m+n
m
+
n
?
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trapezium
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