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A chord is a straight line from one point on a circle's circumference to another. Because the largest straight line distance in a circle is the diameter and the diameter is also a chord, the diameter is the longest chord.

Join the endpoints of a given chord to the center of the circle to form an isosceles triangle. The triangle inequality then tells that the length of the chord is less than two radii of the circle, i.e., less than the diameter.

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Q: Why is the diameter the longest chord?
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