MathDB

Let

ABC

be an acute-angled triangle. The external bisector of

\angle BAC

meets the line

BC

at point

N

. Let

M

be the midpoint of

BC

P

and

Q

are two points on line

AN

such that,

\angle PMN=\angle MQN=90^{\circ}

. If

PN=5

and

BC=3

, then the length

QA

can be expressed as

\frac{a}{b}

where

a

and

b

are co-prime positive integers. What is the value of

(a+b)

Problem Statement