# CAT Practice : Coordinate Geometry

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## Circles

Q.39:
In the above figure which of the following holds good?
1. ∠SQO = ∠ROP
2. 2 ∠ROP = ∠SOR
3. ∠POR = ∠ASO
4. ∠QOX’ = ∠SOR + ∠ROP

Choice (A). ∠SQO = ∠ROP

## Detailed Solution

In the figure,

Let ∠ POX = x° , ∠ROP = y°
∴ From properties of circle,
∠POX = ∠PQO = x°
And, ∠ROX = ∠RSO = x° + y°
Now, in ∆ SQO, ∠ RSO is the exterior angle
∴ ∠SQO + ∠SOQ = x + y
=) x + ∠SOQ = x + y
=) ∠ SOQ = y = ∠ROP

Correct Answer: (A). = ∠SQO = ∠ROP

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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.