All chords have the same length, so their midpoints are at the same distance from the centre of the circle. Therefore, the midpoints of all such chords form a circle concentric with the given circle.
Consider all chords of a circle of a fixed length. What is the shape formed by the midpoints of all these chords?
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Consider chords of a fixed length in a circle with centre O and radius r. The perpendicular from O to each chord bisects it. Since all chords have the same length, each half-chord has the same length. Hence, by the right triangle relation, the distance of every chord’s midpoint from O is the same. Therefore, all the midpoints lie on a circle having O as its centre. Thus, they form a concentric circle.
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