Circles: Tangents and Chord Properties Summary Results Circles: Tangents and Chord Properties A circle is a plane figure with a fixed center and a circu...
Circles: Tangents and Chord Properties Summary Results
Circles: Tangents and Chord Properties
A circle is a plane figure with a fixed center and a circumference that encircles this center. A tangent is a line segment that intersects the circle at exactly one point, while a chord is a line segment that connects two points on the circle.
The properties of a circle related to its tangents and chords are summarized below:
The radius: It is the distance from the center to any point on the circle.
The diameter: It is twice the length of the radius.
The circumference: It is the length of the entire circle.
The circumference of a circle is always π times its radius.
The area of a circle is π times the radius squared.
The perimeter of a circle is 2π times its radius.
Tangents and Chord Properties
The following properties relate tangents and chords to each other:
A tangent to a circle at a point P divides the circle into two arcs.
The tangents to a circle from the same point P are all equal in length.
A chord is perpendicular to a tangent at a point P.
The distance from the center to any point on a chord is equal to the radius.
A circle can have multiple tangents passing through a single point.
A circle can have multiple chords with the same endpoints.
These properties demonstrate that circles are a fascinating and versatile geometric shape with many intricate and interconnected features