The longest chord in a circle is the diameter

Chord:- The line segment which is formed by joining any two points present on the circle is called a chord of the circle.

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 in a circle is the diameter

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A is a point outside of a circle with centre O. Cochin Shipyard Executive Trainee.

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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 :. 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. Ambiguously, the word "diameter" also denotes the length of a diameter.

The longest chord in a circle is the diameter

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. Theorem 3: For two unequal chords of a circle, the larger chord will be closer to the center than the smaller chord.

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The diameter of a circle is a line that passes through the center and meets the circumference at opposite ends.

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