CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions | CAT Geometry Questions | Circles
× CAT Questions
CAT Quantitative Aptitude
HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion
DI LR: Bar Graphs DI LR: Pie Charts DI LR: Multiple Graphs DI LR: Word Problems DI LR: Line Graphs DI LR: Sequencing DI LR: Grid Puzzles DI LR: Math Puzzles DI LR: Visualization DI LR: Other Patterns DI LR: CAT 2017 Cet DI LR: CAT 2017 Rural Survey DI LR: CAT 2017 Happiness DI LR: CAT 2017 Airlines DI LR: CAT 2017 Travel Route DI LR: CAT 2017 Food Delivery DI LR: CAT 2017 Square Layout DI LR: CAT 2017 Team Project DI LR: CAT 2017 Assets DI LR: CAT 2017 Pizza DI LR: CAT 2017 Electives DI LR: CAT 2017 Chess DI LR: CAT 2017 Dorms DI LR: CAT 2017 Tea DI LR: CAT 2017 Friends DI LR: CAT 2017 Security Scan
CAT Online Coaching
CAT Question MenuCAT Questions

The question is from the topic circles. It is a data sufficiency question. Finding the angle subtended by a chord at the centre would help. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 32: Find ∠PRB. Given
I. ∠BPQ = 22 and O is the centre of the circle
II. ∠RBP = 54 and chord PQ is parallel to AB

CAT Question - Geometry - circles
  1. Either I or II individually is sufficient
  2. Both I and II together are required
  3. One of the statements alone is sufficient
  4. Need more data

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!

2IIM : Best Online CAT Coaching.

Best CAT Coaching in Chennai

CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!

Explanatory Answer

Method of solving this CAT Question from Circles: Try to find the angle subtended by the chord PB at the center from the given statements!

Statement I
O is the centre implies AB is the diameter
∠BPQ = 22
Let us join OP and see what we get.
CAT Question - Geometry - circles
∠OPB = ∠OBP (Triangle OPB is isosceles)
If only we know ∠POB, then we can find the answer…

Statement II
∠RBP = 54
CAT Question - Geometry - circles
Chord PQ is parallel to AB implies ∠BPQ = ∠ABP
We definitely need one of the above angle to get some clue…
Let us combine both the statements
Since ∠BPQ = 22, ∠ABP = 22
∠POB = 180 – (22 + 22) = 136
∠PRB is nothing but the angle subtended by the chord PB and is half the angle at the center.
∠PRB = ∠POB / 2 = 136/ 2 = 68
We need both statements together to arrive at a solution!

The question is "Choose the correct answer"

Hence, the answer is Both I and II together are required.

Choice B is the correct answer.


CAT Preparation Online | CAT Geometry questions Videos On YouTube

Other useful sources for Geometry Question | Geometry Triangles Circles Quadrilaterals Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now