Q. 124.0( 31 Votes )

Two circles of radii 10 cm and 8 cm intersect each other, and the length of the common chord is 12 cm. Find the distance between their centers.


Answer :

Let,


Radius OA = 10 cm and O’A = 8 cm


Chord AB = 12 cm


Now,


AD = (1/2) AB


AD = (1/2) 12 = 6 cm


In triangle OAD,


OD2 = OA2 - AD2


OD2 = 102 - 62


OD2= 100 - 36


OD2= 64


OD = 8 cm


In triangle O’AD,


O’D2 = O’A2 - AD2


O’D2 = 82 - 62


O’D2= 64 - 36


O’D2= 28


O’D = 2 √7 cm


Now,


OO’ = OD + O’D =


Hence, distance between their centers =


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