Chord
A chord is a line segment that connects two points on the circumference of a circle
A chord is a line segment that connects two points on the circumference of a circle. It is formed by drawing a straight line between two points on the circle. The two points that define a chord are called the endpoints of the chord.
In geometry, a chord is an important concept as it helps in understanding various properties of circles. Some key points about chords include:
1. Diameter: A chord that passes through the center of the circle is called a diameter. It is the longest possible chord in a circle, and it divides the circle into two equal halves. The length of a diameter is twice the length of a radius.
2. Secant: A line that intersects a circle at two distinct points is called a secant. A secant can be considered as an extended chord that passes through the circle.
3. Tangent: A line that touches a circle at only one point is called a tangent. Unlike a chord or a secant, a tangent does not intersect the circle. The point where the tangent touches the circle is called the point of tangency.
Properties of Chords:
– In a circle, the perpendicular bisector of a chord passes through the center of the circle.
– The perpendicular from the center of a circle to a chord bisects the chord.
– Two chords that are equidistant from the center of the circle are congruent.
– If two chords in a circle are congruent, their corresponding arcs are also congruent.
Chords are used in various mathematical applications, including geometry, trigonometry, and calculus. Understanding the properties of chords helps in solving problems related to circles and determining the relationships between different parts of a circle.
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