MathDB

IOQM 2023-24 P-15

Source:

September 3, 2023

Problem Statement

Let

A B C D

be a unit square. Suppose

M

and

N

are points on

B C

and

C D

respectively such that the perimeter of triangle

M C N

is 2 . Let

O

be the circumcentre of triangle

M A N

, and

P

be the circumcentre of triangle

M O N

. If

\left(\frac{O P}{O A}\right)^2=\frac{m}{n}

for some relatively prime positive integers

m

and

n

, find the value of

m+n

.

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