Given a circle centre O and a point P in its interior, the midpoints of all the chords passing through P lie on a circle, which also passes through P and through O.
Given a circle centre O and a point P in its interior, the midpoints of all the chords passing through P lie on a circle, which also passes through P and through O.
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On Quora someone asked for a proof of this, which I will put in another post.