Question

two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. find the distance between their centres.

Answer 1

hey
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given radius

OP = 10 cm
O'P = 8 cm

•by theorem we know that a line joining from centre to chord is always perpendicular bisector of chord

so PL=LQ = 6cm

now see the attached file

hope helped
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Answer 2

Answer:

Center of circles= O and O'

Radii = 10 and 8cm

common chord= PQ

OP= 10cm

O'P = 8cm

PQ= 12cm

PL= 1/2PQ

= 1/2 x 12

= 6cm

In right angle triangle OLP  

OP² = OL² + LP²

OL= √OP² - LP²  

= √10²- 6²

= √64

= 8cm

In right angle triangle O'LP

O'P²= O'L² - LP²

O'L= √O'P² - LP²

= √8² - 6²

= √28

= 5.29 cm

OO'= 8 + 5.29  

= 13.29 cm

Step-by-step explanation: hope it helps u