Question

two circles of radius 6cm and 8cm intersect at a and b if the distance between their centres is 10 cm find the length of common chord AB




please help its urgent ​

Answer 1

Answer:

Given: OA = 10 cm, O'A = 8 cm and AB = 12 cm

A

D

=

A

B

2

=

12

2

=

6

c

m

Now, in right angled Δ ADO, we have:

O

A

2

=

A

D

2

+

O

D

2

⇒

O

D

2

=

O

A

2

−

A

D

2

=

10

2

−

6

2

= 100 - 36 = 64

∴ OD = 8 cmSimilarly, in right angled Δ ADO', we have:

O

′

A

2

=

A

D

2

+

O

′

D

2

⇒

O

′

D

2

=

O

′

A

2

−

A

D

2

=

8

2

−

6

2

= 64 - 36

= 28

Thus, OO' = (OD + O'D )

= 8+27 cm

Hence, the distance between their centres is 8+27cm.

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