Math's: Circle: Meaning of a Circle, Parts of a Circle, Concentric and Congruent Circles

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Meaning of a Circle

A circle is a collection of all points in a plane which are at a constant distance from a fixed point in the same plane.

Meaning of a Circle

Meaning of a Circle

Parts of a Circle

Radius- A line segment joining the center of the circle to a point on the circle is called its radius. All radii of a circle are equal. In the following circle and are two radii and

Parts of a Circle

Parts of a Circle

Circumference – The perimeter i.e. the length of the boundary of a circle is called its circumference. If P is point on a circle and this point moves along the circle once and comes back to its original position, then the distance covered by P is called the circumference of the circle.

Parts of a Circle

Parts of a Circle

Interior of a Circle and Exterior of a Circle- The inner part of the circle i.e. the one lying within the circumference is called the interior of the circle and the outer part of the circle i.e. the one lying outside the circumference is called the exterior of the circle.

Parts of a Circle

Parts of a Circle

Chord- A line segment joining any two points of a circle is called a chord. are the three chords of the circle given below.

Parts of a Circle

Parts of a Circle

  • Diameter- A chord passing through the center of a circle is called its diameter. A diameter is the longest chord of the circle and is double the radius. In the above circle, is the diameter.

  • Semicircle- Half of a circle is called a semicircle. A diameter divides the circle into two parts. Each part is called a semicircle. is a semicircle in the circle given below.

Parts of a Circle

Parts of a Circle

Arc- Any part of a circle is called an arc. If it is greater than that of its semicircle then it is called a major arc and if it is smaller than that of its semicircle, it is called a minor arc. is an arc in the below circle.

Parts of a Circle

Parts of a Circle

Sector- The region bounded by an arc of a circle and two radii at its end points is called a sector. If it is greater than that of its semicircle then it is called a major sector and if it is smaller than that of its semicircle, it is called a minor sector. In the circle given below, the shaded region indicates a minor sector whereas the unshaded region is a major sector.

Parts of a Circle

Parts of a Circle

Segment- A chord divides the interior of a circle into two parts, each of which is called a segment. The bigger part is called a major segment and the smaller part is called a minor segment. In the following circle, the shaded portion is a minor segment whereas the unshaded portion is a major segment.

Parts of a Circle

Parts of a Circle

Concentric Circles and Congruent Circles

Concentric Circles-Circles having the same center, but different radii are called concentric circles.

Concentric Circles

Concentric Circles

Congruent Circles- Two or more circles having same radii are known as Congruent Circles. We can superimpose (place) one over the other such that they cover each other completely.

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