CAT Practice : Geometry-Triangles

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Triangles  Question 14
Hexagon inscribed inside circle

Chords of a circle

    Q.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. 63
    2. 43
    3. 83
    4. 23

 

  • Correct Answer
    Choice (B). 43

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution



OM = 3, OS = 5

MS = 4 = RM {Using Pythagoras theorem}

=> RS = 8 cms

TS = 1/3 of RT

TS = 1/4 of RS

If RS = 8 cms

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 x TQ)

(PT+TQ)/2 ≥ √12

PT + TQ ≥ 2√12

=> PQ ≥ 2√12

Or PQ ≥ 4√3

Minimum PQ = 4√3

Answer choice (b).

Correct Answer: 43



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.