CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions

The question is from the topic circles. It tests the understanding of the concept angles. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. We have to verify the following options and choose the correct one.

Question 39: In the below figure which of the following holds good?

1. ∠SQO = ∠ROP
2. 2 ∠ROP = ∠SOR
3. ∠POR = ∠ASO
4. ∠QOX’ = ∠SOR + ∠ROP

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Explanatory Answer

Method of solving this CAT Question from Circles: Knowing properties of circle would help.

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

The question is "In the figure which of the following holds good?"

Hence, the answer is ∠SQO = ∠ROP.

Choice A is the correct answer.