Question : Two circles of the same radius 6 cm, intersect each other at P and Q. If PQ = 10 cm, then what is the distance between the centres of the two circles?
Option 1: $10\mathrm{~cm}$
Option 2: $8\mathrm{~cm}$
Option 3: $6\sqrt{11} \mathrm{~cm}$
Option 4: $2\sqrt{11} \mathrm{~cm}$
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Correct Answer: $2\sqrt{11} \mathrm{~cm}$
Solution :
Two circles meet at P and Q, with PQ = 10 cm
Radii, AP = BP = 6 cm
We know perpendicular from the centre to a chord bisects the chord.
So, PM = 5 cm
Distance between the two circles = AB = AM + BM = 2 × AM (by symmetry)
For AM, consider triangle OPM,
AP
2
= AM
2
+ PM
2
⇒ 6
2
= AM
2
+ 5
2
⇒ AM = $\sqrt{11}$
⇒ AB = $2\sqrt{11}$ cm
Hence, the correct answer is $2\sqrt{11}$ cm.
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