Re: Distinct points P, Q, R, S lie on the circle x^2 + y^2 = 25 and have

Points P,Q,R and S have integer coordinates and they lie on a circle of radius 5 and origin as center .

Possible coordinates for point P,Q,R and S are ={(5,0),(4,3,),(3,4),(0,5),(-3,4),(-4,3),(-5,0),(-4,-3),(-3,-4),(0,-5),(3,-4),and (4,-3)}

For PQ/RS to be max ...PQ has to be max and RS has to be minimum and both distances are to be irrational values

Since Distance PQ and RS are to be irrational ..PQ and RS can not be diagonal as in that case value =10 will be rational.
Lets check next possible distance but both diagnol ..say points (4,3) and (-3,-4) distance is 7Sq Root(2) a irrational value ...

Now for RS let us take two immediate points say (-3,4) and (-4,3) distance is sqrot(2)

Ratio of PQ/RS is =7...hence answer is D