For the diagram,
PQ = diameter of the circle, as it is passing through the centre

OR = OS = Radius of the circle and \(\angle ROS\) = 90°.

so the\(\triangle ORS\) is a 45°-90°-45°

and the sides are divided in \(1 : 1 : \sqrt2\)

therefore \(OR = OS = 1\) and \(RS = \sqrt 2\)

and\(PQ = 1 + 1 = 2\)


Now QTY A =\(\frac{PQ}{RS}= \frac{2}{\sqrt2} = \sqrt2 = 1.44\)

QTY B = 2

Therefore \(QTY A < QTY B.\)

OPtion B.
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Tricky

Hi,

You can solve this question without assuming the value or without doing a tedious calculation.

Consider this we know RO and RS is the radius and PQ is the diameter.
As ROS is a right triangle the right angle has to be formed at angle ROS as the other two lengths are same, which makes this a 45-45-90 triangle. Thus RS has to be greater than RO.

Quantity A:

PQ/RS= 2 RO/RS
RS is root 2 times RO which is around 1.414
2/1.414- This is surely give us a value less than QTY B i.e 2

Hope this helps