Mathematics
Show that the diameter is the greatest chord of a circle.
Circles
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Answer
Let AB be a diameter of the circle and O be the centre.
By definition, it passes through the center, so AB = OA + OB = r + r = 2r.
Let CD be any other chord of the circle that does not pass through the center.
∴ OC = OD = r
The sum of the lengths of any two sides must be greater than the length of the third side.
OC + OD > CD
2r > CD
AB > CD
This proves the length of the diameter is always greater than the length of any other chord that does not pass through the center.
Hence, the diameter is the greatest chord of a circle.
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