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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

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Explanatory Answer

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

Geometry - triangles: CAT Geometry Altitude of a Triangle
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.


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