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