# CAT Practice : Coordinate Geometry

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Lines and Geometry

## Basic Geometry

Q.40: In the below figure:-

If ${\frac{PQ}{PR} = \frac{PR}{RQ}}$ , then
1. ${\frac{PR}{QR}} > 2$
2. ${\frac{PR}{QR}} = 2$
3. ${\frac{PR}{QR}} < 2$
4. can’t be determined

Choice (C). ${\frac{PR}{QR}} < 2$

## Detailed Solution

In the figure,

Given, ${\frac{PQ}{PR} = \frac{PR}{RQ}}$
Here, PQ = PR + RQ
=) 1 + ${\frac{RQ}{PR} = \frac{PR}{RQ}}$
Let ${\frac{PR}{RQ}}$ = x
=) 1 + ${\frac{1}{x}}$ = x
=) x +1 = x2
=) x2 – x – 1 = 0
=) x = ${\frac{(+1 ± √(1+4))}{2} = \frac{(1±√5)}{2}}$ Since PR – RQ > 0
=) x = ${\frac{(1+√5)}{2}}$ which is between 1 and 2

Correct Answer: (C). = ${\frac{PR}{QR}} < 2$

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.