Prove that the length of the common chor...

Prove that the length of the common chord of the two circles :
`(x-a)^(2)+(y-b)^(2)=c^(2)and(x-b)^(2)+(y-a)^(2)=c^(2)" is "sqrt(4c^(2)-2(a-b)^(2))`
Find also the condition when the given circles touch.

A

`sqrt(4c^2+2(a-b)^2)`

B

`sqrt(4c^2+2(a+b)^2)`

C

`sqrt(4c^2-2(a-b)^2)`

D

`sqrt(c^2-(a-b)^2)`

Verified by Experts

The correct Answer is:

C

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