Question

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm and 34 cm, calculate the distance between their centers.

Answer 1

OA = 25 cm and AB = 30 cm

∴    AD = `1/2 xx "AB"  = (1/2 xx 30)` cm = 15 cm 

Now in right angled ADO
OA² + AD² + OD²  
⇒  OD² = OA² - OD²  = 25² - 15² 
             = 625 - 225 = 400
∴ OD = `sqrt 400` = 20 cm
Again, we have  O'A = 17 cm.

In right-angle ADO'
O'A² = A'D² + O'D²  
⇒  O'D² = O'A² - AD² 
= 17² - 15² 
= 289 - 225 = 64

∴ O'D = 8 cm
∴ OO' = ( OD + O'D )
          = ( 20 + 8 ) = 28 cm

∴ the distance between their centres is 28 cm.