The longest chord of the circle

Geometry is the major part of mathematics that deals with lines, angles, points, etc. They are the visual study of shapes and sizes. The geometric approach is seen everywhere around us as every object has a certain shape whose parameters can be studied with the help of geometrical formulas.

Indeed why? Why a diameter is the longest chord in a circle? I sometimes heard and several times read at popular math sites that the reason why a diameter is the longest chord is that a diameter passes through the center of the circle. While that is true that passing through the center has something to do with the length of a chord, the answer, as given, is vacuous. Since the definition of a diameter is a chord passing through the center of the circle, such an explanation actually reads: "The diameter is the longest chord in a circle because it is a diameter of the circle. Let's recollect the definitions :.

The longest chord of the circle

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Take a string and tape its ends anywhere inside the hula hoop. That string represents a chord of the circle! The longest chord you could make would stretch from one side of the hula hoop to the other, passing through the center. At this point, students begin studying the chord and other parts of circles. That deals with shapes, sizes, properties of space, and the relationships between different forms. The study of the chord of a circle aligns with the following Common Core Standards :. A chord of a circle is a line segment whose endpoints lie on the circle. Perpendicular bisectors of a chord always pass through the center of the circle. The longest chord of a circle passes through the center of the circle. This chord is what we know as the diameter.

The longest chord of the circle

The chord of a circle is defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle. A line segment that joins two points on the circumference of the circle is defined as the chord of the circle. Among the other line segments that can be drawn in a circle, the chord is one whose endpoints lie on the circumference. Observe the following circle to identify the chord PQ. Diameter is also considered to be a chord which passes through the center of the circle. Theorem 1: The perpendicular to a chord, drawn from the center of the circle, bisects the chord. Observe the following circle to understand the theorem in which OP is the perpendicular bisector of chord AB and the chord gets bisected into AP and PB. Theorem 2: Chords of a circle, equidistant from the center of the circle are equal.

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The longest chord of a circle is its diameter, which is double the radius of the circle. Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the center is always greater than the more remote. Related Articles. Incidentally, Euclid proved that statement in the third book of his Elements as a more informative Proposition XV :. Similar Reads. Since the definition of a diameter is a chord passing through the center of the circle, such an explanation actually reads: "The diameter is the longest chord in a circle because it is a diameter of the circle. Circle Theorems. Vote for difficulty :. You can suggest the changes for now and it will be under the article's discussion tab. Question 2: Determine the diameter of a circle with a radius of 12cm. Mathematically it can be written as,. Create Improvement. Like Article Like.

There are many parts of a circle that make it a circle.

Givental, Kiselev's Geometry. Improve Improve. Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the center is always greater than the more remote. Hence, it can also be stated that shapes are the collection of points. Why a diameter is the longest chord in a circle? While that is true that passing through the center has something to do with the length of a chord, the answer, as given, is vacuous. Easy Normal Medium Hard Expert. Let's recollect the definitions :. What is the longest chord of a Circle? A segment of a straight line joining two points on a circle is called a chord ; a chord that passes through the center of the circle is called a diameter.