MathDB

The circle

x^2+ y^2 = r^2

meets the coordinate axis at

A = (r,0), B = (-r,0), C = (0,r)

and

D = (0,-r).

Let

P = (u,v)

and

Q = (-u,v)

be two points on the circumference of the circle. Let

N

be the point of intersection of

PQ

and the

y

-axis, and

M

be the foot of the perpendicular drawn from

P

to the

x

-axis. If

r^2

is odd,

u = p^m > q^n = v,

where

p

and

q

are prime numbers and

m

and

n

are natural numbers, show that

|AM| = 1, |BM| = 9, |DN| = 8, |PQ| = 8.

Problem Statement