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Can a chord of a circle also be the diameter of the circle?
Sure. Any chord that passes through the center of the circle is also a diameter. Chords can have many different lengths, but a diameter is the longest chord.
What is the radius of a circle in which the longest chord has length y?
longest chord = diameter y = longest chord y = diameter radius = 1/2 diameter therefore, radius = 1/2y
What is a segment that has both endpoints on a circle?
A chord of which the circle's diameter is the largest chord
Why is the diameter the longest chord?
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. See related links.
Is the diameter the longest chord?
Yes
