Two circles of radii 5 cm …

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Two circles of radii 5 cm and 3 cm intersect at two points and the difference between their centres is 4 cm. Find the length of the common chord.
In the solution, if the common chord is on the centre of circle 2 then clearly it is the diameter. So 2×radius of circle 2 is the length of the chord.
Then, why we need to show that O' is the mid point of the common chord AB???
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