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If two circles intersect at two points,...

If two circles intersect at two points, prove that their centres lie on the perpendicularbisector of the common chord.

Text Solution

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`AB` is the chord of the circle centered at `O` and it is also the chord of the circle centered at `O’`.
Let `OO'` intersect `AB` at `M`.
In `/_\OAO'` and `/_\OBO'`, we have
`OA = OB` (radii of same circle)
`O'A = O'B` (radii of same circle)
`OO' = OO'` (common)
Triangle `OAO'` and `OBO'` are congruent by side side side congruency.
`/_AOO' =/_BOO'`
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