Two circles with centres A and B,of radii 5cm and 3cm touch each other internally.If the perpendicular bisector of AB meet the bigger circle at M and N,find the length of MN.

Asked by  | 28th Feb, 2012, 04:08: PM

Expert Answer:

Let O be the point of contact of both the circles.
Then AO = 5 cm and BO = 3 cm
Thus, AB 5 - 3 = 2 cm
Let MN bisect AB at P, then AP = 1 cm
Now in right triangle APM, AP = 1 cm and AM = 5 cm
therefore MP2 = 52 - 12 = 25 - 1 = 24 
That is MP = sq. root (24)
Hence, MN = 2*sq. root (24)

Answered by  | 28th Feb, 2012, 04:24: PM

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