MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2023-24 IOQM India
15
15
Part of
2023-24 IOQM India
Problems
(1)
IOQM 2023-24 P-15
Source:
9/3/2023
Let
A
B
C
D
A B C D
A
BC
D
be a unit square. Suppose
M
M
M
and
N
N
N
are points on
B
C
B C
BC
and
C
D
C D
C
D
respectively such that the perimeter of triangle
M
C
N
M C N
MCN
is 2 . Let
O
O
O
be the circumcentre of triangle
M
A
N
M A N
M
A
N
, and
P
P
P
be the circumcentre of triangle
M
O
N
M O N
MON
. If
(
O
P
O
A
)
2
=
m
n
\left(\frac{O P}{O A}\right)^2=\frac{m}{n}
(
O
A
OP
)
2
=
n
m
for some relatively prime positive integers
m
m
m
and
n
n
n
, find the value of
m
+
n
m+n
m
+
n
.