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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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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
Is the diameter the longest chord?
Yes
What is the longest chord that can be drawn on a circle?
The diameter (across the widest part) is the longest chord that can be drawn on a circle.
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.
Is every chord of a circle also a diameter?
No. The chord is a diameter only if it passes through the center of the circle. In that case,it's also the longest that any chord can possibly be in that circle.
