The longest chord of a circle is its diameter.
Here's why and how to find it:
A chord is a line segment that connects two points on the circumference of a circle. The diameter is a special chord that passes through the center of the circle. Since any other chord will necessarily be shorter than the one passing directly through the center, the diameter is always the longest.
Finding the Longest Chord (Diameter):
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Locate the center of the circle. If you have a physical circle, you can find the center by folding the circle in half twice; the intersection of the folds is the center. If you have a mathematical representation of the circle (e.g., an equation), the center will be part of the equation.
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Draw a straight line through the center. Any straight line that passes through the center of the circle and extends to meet the circumference at two points is a diameter (and therefore the longest chord).
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Measure the distance between the two points where the line intersects the circumference. This measurement is the length of the diameter, which is the longest chord.
Relationship to Radius:
- The diameter is twice the length of the radius of the circle. (Diameter = 2 * Radius)
- If you know the radius, simply multiply it by 2 to find the length of the longest chord (diameter).
Example:
If a circle has a radius of 5 cm, then its longest chord (diameter) is 2 * 5 cm = 10 cm.
In Summary:
The longest chord of a circle is its diameter. To find it, locate the center of the circle and draw a line through it, connecting two points on the circumference. The length of this line is the length of the longest chord.
