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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