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.

Question

Philoid · Accepted 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 =