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
CAT DILR
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 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 Cet DI LR: CAT 2017 Rural Survey DI LR: CAT 2017 Happiness

CAT Online Coaching
CAT Question MenuCAT Questions

The question is from the topic circles. In this problem details about two perpendicular chords are given and we have to find out the radius of the circle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Knowing chord intersection theorem helps.

Question 19: Two mutually perpendicular chords AB and CD intersect at P. AP = 4, PB = 6, CP = 3. Find radius of the circle.

  1. 31.25(1/2)
  2. 37.5(1/2)
  3. 26(1/2)
  4. 52(1/2)

Online CAT Coaching for CAT 2019


Signup to avail 9 full classes Free


CAT Coaching in Chennai


Starts Sat, Feb 23, 2019


Explanatory Answer

Method of solving this CAT Question from Circles: Figure out the diagram and then the question becomes very easy.
CAT Question - Geometry - Circles

When 2 chords AB and CD intersect at P then AP * PB = CP * PD
Hence 4 * 6 = 3 * PD
Thus, PD = 8
Now AB = AP + PB = 10
And CD = CP + PD
Thus, CD = 11
Consider the circle with center O.
Drop a perpendicular from O to chord AB and CD.
This will bisect the chords at X and Y i.e AX=XB and CY = YD.
Here AX = AP + PX i.e 5 = 4 + PX
PX = 1
Similarly, since CD = 11, PY+CP+YD = 11,
=> PY = 11-3-5.5 = 2.5.
PY = OX and PX = OY.
So, PXOY will from a rectangle as seen in the figure.
Now consider the triangle BOX, it is a right triangle where OB is the radius.
XB = 5, OX = 2.5
Then OB = ( OX2 + XB2 )1/2 OB = 31.251/2 Thus radius = 31.251/2 The radius can also be found out using the triangle YOD.

The question is "Find radius of the circle."

Hence, the answer is 31.251/2.

Choice A is the correct answer.

 

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Feb 23rd, 2019

★ CAT Coaching Info

CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo


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,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com