# Two circles Γ and ∑, with centres O and O', respectively, are such that O' lies on Γ. Let A be a point on ∑ and M the midpoint

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Two circles Γ and ∑, with centres O and O', respectively, are such that O' lies on Γ. Let A be a point on ∑ and M the midpoint of the segment AO'. If B is a point on ∑ different from A such that AB is parallel to OM, show that the midpoint of AB lies on Γ.

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Also OK = OO' (radii of circle Γ)

or KA = KB