A __________ of a circle is a line segment joining any two points on t...
A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse.
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A __________ of a circle is a line segment joining any two points on t...
A chord of a circle is a line segment that connects any two points on the circumference of the circle. It is one of the basic elements of a circle and has several important properties and applications in geometry. Let's explore this concept in more detail.
Chord:
A chord can be defined as a line segment with its endpoints lying on the circumference of a circle. It is important to note that a chord does not necessarily pass through the center of the circle. The length of a chord can vary depending on the positions of its endpoints.
Properties of a Chord:
1. Length: The length of a chord can be longer or shorter than the radius of the circle, depending on its position. If the chord passes through the center of the circle, it is called the diameter, which is the longest possible chord. Any other chord will have a length that is less than the diameter but greater than the radius.
2. Perpendicular Bisector: The chord of a circle can be divided into two equal halves by a line called the perpendicular bisector. This line passes through the midpoint of the chord and is perpendicular to the chord itself.
3. Intercepted Arc: A chord divides the circumference of a circle into two arc segments. These segments are called intercepted arcs. The two intercepted arcs are unequal in length, and their lengths depend on the position of the chord.
Applications of Chords:
1. Geometry: Chords are used extensively in geometric calculations and constructions. They are used in the derivation of theorems, such as the Inscribed Angle Theorem and the Intersecting Chords Theorem.
2. Music: In music theory, a chord is a combination of three or more musical notes played simultaneously. The term "chord" is derived from its geometric counterpart, as the different notes played together can be seen as points on a circle.
To summarize, a chord of a circle is a line segment connecting any two points on the circumference of the circle. It has various properties and applications in geometry and music.
A __________ of a circle is a line segment joining any two points on t...
Diameter is the correct answer
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