The term "circle" refers to a shape in Euclidean geometry. It is defined as the set of all points in a plane that are equidistant from a given point, called the center. Here are some key characteristics and properties of a circle:
Basic Characteristics:
Center: The point from which all points on the circle are equidistant.
Radius: The distance from the center to any point on the circle.
Diameter: The distance across the circle through the center, which is twice the radius.
Chord: A line segment whose endpoints are on the circle.
Tangent: A line that touches the circle at exactly one point without crossing it.
Secant: A line that intersects the circle at two points.
Properties:
The circumference of a circle is given by the formula ( C = 2pi r ), where ( r ) is the radius.
The area of a circle is given by the formula ( A = pi r2 ).
A circle is the set of all points at a fixed distance from a given point (the center).
The longest chord in a circle is the diameter.
The angle subtended by a diameter at any point on the circle is a right angle (90 degrees).
All radii of a circle are congruent.
The sum of opposite angles in a cyclic quadrilateral (a quadrilateral whose vertices all lie on a circle) is 180 degrees.
Applications:
Circles are fundamental in many areas of mathematics, physics, engineering, and everyday life. They are used to model situations where uniformity and symmetry are important, such as in the wheels of vehicles, the orbits of planets, and in various scientific and engineering calculations.
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