CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions | CAT Geometry Questions | Polygon and 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 and polygons.It discusses about the ratio of circumference of circle to the polygon that is inscribed in it. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 35: There are 2 concentric circles, one big and one small. A square ABCD is inscribed inside the big circle while the same square circumscribes the small circle. The square touches the small circle at points P, Q, R and S. Determine the ratio of circumference of big circle to the polygon PQRS.

  1. π : 2
  2. 2 : π
  3. 2 : √2
  4. π : √2

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: Finding out what shape is PQRS and assuming the side of ABCD to be 2a will help to get further answer!
CAT Question - Geometry - circles

Let the side of the square ABCD be 2a.
A line from the centre will bisect the chords AB, BC, CD and DA
Therefore AP = PB = a. Similarly for other sides too.
From the above we can conclude that PQ = QR = RS = SP. Therefore PQRS is also a square.

Radius of big circle = diagonal of the square APOS = a√2
Circumference = 2π * a√2
Now we have to find the side of square PQRS.
We know that radius of small circle = side of the square APOS = a
Consider triangle PSO. PS2 = OP2 + OS2. Therefore, PS = a√2
Circumference of square with side a√2 = 4a√2
Ratio = 2π * a√2 : 4a√2
=> π : 2

The question is "Determine the ratio of circumference of big circle to the polygon PQRS."

Hence, the answer is π : 2

Choice A 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