MathDB

Two real numbers

a

and

b

are chosen independently and uniformly at random from the interval

(0, 75)

. Let

O

and

P

be two points on the plane with

OP = 200

. Let

Q

and

R

be on the same side of line

OP

such that the degree measures of

\angle POQ

and

\angle POR

are

a

and

b

respectively, and

\angle OQP

and

\angle ORP

are both right angles. The probability that

QR \leq 100

is equal to

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m + n

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