# CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

###### CAT Questions | CAT Geometry Questions | Circles

The question is from CAT Geometry - Circles. It tests our understanding on properties of circles. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. In this question it discusses about the intersecting chords in a circle.

Question 14: A circle of radius 5 cm has chord RS at a distance of 3 units from it. Chord PQ intersects with chord RS at T such that TS = 1/3 of RT. Find minimum value of PQ.

1. 6√3
2. 4√3
3. 8√3
4. 2√3

## Best CAT Coaching in Chennai

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

##### Method of solving this CAT Question from circles: Remembering some theorems would come as handy in situations.

OM = 3, OS = 5
MS = 4 = RM {Using Pythagoras theorem}
=> RS = 8 cms
TS = 1/3 of RT
TS = 1/4 of RS
TS = 2 cms
RT * TS = PT * TQ
{Intersecting Chords theorem: When there are two intersecting chords, the product of the rectangle formed by the segments of one chord is equal to the product of the rectangle formed by the segments of the other.}
6 × 2 = PT * TQ
PT * TQ = 12
By AM – GM inequality, (PT+TQ)/2 ≥ √(PT * TQ)
(PT+TQ)/2 ≥ √12
PT + TQ ≥ 2√12
=> PQ ≥ 2√12
Or PQ ≥ 4√3
Minimum PQ = 4√3

The question is " Find minimum value of PQ."

##### Hence, the answer is 4√3.

Choice B is the correct answer.

###### CAT Coaching in ChennaiCAT 2023

Classroom Batches Starting Now! @Gopalapuram

###### Best CAT Coaching in Chennai Introductory offer of 5000/-

Attend a Demo Class

## CAT Preparation Online | CAT Geometry questions Videos On YouTube

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

##### 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
Email: prep@2iim.com