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,

OD^{2} = OA^{2} - AD^{2}

⇒ OD^{2} = 10^{2} - 6^{2}

⇒ OD^{2}= 100 - 36

⇒ OD^{2}= 64

⇒ OD = 8 cm

In triangle O’AD,

O’D^{2} = O’A^{2} - AD^{2}

⇒ O’D^{2} = 8^{2} - 6^{2}

⇒ O’D^{2}= 64 - 36

⇒ O’D^{2}= 28

⇒ O’D = 2 √7 cm

Now,

OO’ = OD + O’D =

Hence, distance between their centers =

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