Circle and its related terms

circle


A circle is the locus of a point which moves such that its distance from a fixed point is always constant.

The fixed point is called the center and the fixed distance is called the radius of the circle.

The circle has center O and OA is the radius of r units.

Radius

A line segment joining the center of a circle to a point on the circle is called the radius of the circle.

Circumference

The perimeter or the length of the boundary of the circle is called its circumference.
The circumference of a circle with radius r is 2πr units.



Circle Chord and Diameter

Chord

A line segment joining any two points on the circle is called the chord of the circle.

NT and RS are chords of the circle.

Diameter

A chord passing through the center of the circle is called the diameter of the circle.

POQ is diameter of the circle.

diameter = 2×radius
Diameter is the largest chord of the circle.

semi circle

Semi-Circle

The diameter of a circle divide it into two equal parts. Each part is called a semi-circle.

ACB and ADB are semi-circles.
arcs of the circle

Arc of a circle

The part of a circle included between two points on it is called the arc of the circle.

CDE is arc of the circle. There are two arcs formed when the circle is divided by two points.

Minor Arc

The arc CDE is called the Minor arc as its length is less then the other arc.

Major Arc

The arc EFC is called the Major arc as its length is more then the other arc.

The minor arc and major arc when joined give the circle.

sector of a circle

Sector of a circle

The area enclosed by an arc and the radii to the endpoints of the arc is called the sector of the circle.

Here, OCDE is a sector of the circle enclosed by arc EDC and radii OC and OE.
segments

Segments

The part of the circle enclosed by an arc and chord joining the end points of the arc is called a segment.

Minor Segment

The segment which is smaller is called the minor segment.

Major Segment

The segment which is bigger is called the major segment.

A segment having the center of the circle is the major segment.

central angle

Central angle

The angle subtended by an arc at the center of the circle is called the central angle. Here, AB subtend ∠AOB at the center of the circle. ∠AOB = θ.
secant and tangent

Secant of a circle

A line which intersect a circle at to distinct points is called the secant of the circle.
PQ is a secant of the circle.

Tangent to a circle

A line that touches a circle at only one point is called the tangent to the circle.
TAU is tangent to the circle.

Facts about tangents

  1. One and only one tangent can be drawn to a circle from a point on it.
  2. Only two tangents can be drawn from a point outside it.
  3. No tangents can be drawn to a circle from a point inside it.

Angle in a semicircle is 90°




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