Shape which can made with any centre and with any radius is known as circle

Circle:

A circle is a two-dimensional geometric shape that is defined as a set of points in a plane that are equidistant from a fixed center point.




Definition:

A circle is a closed curve that is perfectly round and has no corners or edges. It is formed by taking all the points in a plane that are at a fixed distance, called the radius (r), from a central point, known as the center (O).




Key Characteristics of a Circle:

- Center: The center is the point in the plane from which all points on the circle are equidistant. It is typically denoted by the letter 'O'.

- Radius: The radius is the distance from the center of the circle to any point on the circumference. It is always constant and denoted by the letter 'r'.

- Circumference: The circumference is the distance around the outer boundary of the circle. It is calculated using the formula C = 2πr, where 'C' represents the circumference and 'π' represents the mathematical constant pi (approximately 3.14159).

- Diameter: The diameter is a straight line segment passing through the center of the circle and connecting two points on the circumference. It is twice the length of the radius and is denoted by the letter 'd'. The formula for calculating the diameter is d = 2r.

- Chord: A chord is a straight line segment that connects two points on the circumference. It does not necessarily pass through the center of the circle.

- Sector: A sector is a region of the circle enclosed by two radii and an arc.

- Arc: An arc is a curved portion of the circumference.

- Tangent: A tangent is a straight line that touches the circle at only one point.




Properties of a Circle:

- The sum of the interior angles of any polygon inscribed in a circle is equal to 360 degrees.

- The tangent to a circle is perpendicular to the radius drawn to the point of tangency.

- The length of an arc is proportional to the measure of its central angle.

- The radius perpendicular to a chord bisects the chord.

- The opposite angles of a cyclic quadrilateral (quadrilateral inscribed in a circle) are supplementary.




In conclusion, a circle is a fundamental geometric shape that is defined by its center, radius, and the set of points equidistant from the center. It has various key characteristics, properties, and relationships with other geometric elements, making it an essential concept in mathematics.