CBSE Class 6 Mathematics – 18. Circle (Notes)

 

Revision Notes on Circle

Learning Goal

Circles

Interior and Exterior of the Circles

Parts of Circles (Centre, Radius, Chord, Diameter, Circumference, Arc, Sector, Secant, Segment, Semicircle)

Concentric Circle

Tangent, Point of tangent

Circles

The path of noncollinear points that are equidistance from a fixed point is called circle.

Interior of the Circle – Area inside the boundary of the circle is called the Interior of the Circle.

The Exterior of the Circle – Area outside the boundary of the circle is called the Exterior of the Circle.

Parts of Circles

1. Centre – The fixed point is called centre.

2. Radius – The line joining centre and a point of circumference is called radius. Radii is the plural of ‘radius’.

3. Chord – The line joining two points of circumference is called chord.

4. Diameter – The chord passing from centre of circle is called diameter.

Diameter is the longest chord.

5. Circumference – The boundary of the circle is called circumference.

Relation between Circumference and Diameter:

Circumference of a circle is slightly more than three times of its diameter.

Relation between Diameter and Radius: – Diameter of a circle is twice of its radius.

Formula: –

Diameter = 2 × radius

 OR    Radius =

6. Arc – The portion of the boundary of the circle is called arc.

An arc is usually named by 3 points.

Arc ACB is denoted as-

7. Sector– The region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called sector.

There are two types of sectors 1^st is Major & 2^nd is Minor sector

 

8. Secant: –  A line that intersect a circle at two distinct points is called secant.

A line can meet a circle at most in two distinct points. (In fig AB is secant)

9. Segment – The region in the interior of the circle enclosed by an arc and a chord is called segment.

Semi-circle

The half of the circle is called semi-circle.

A diameter divides the circle into two equal parts or semi-circles.

The semicircle enclosed by a diameter and semi arc.

Concentric Circle: – Two or more circle with same radius are called concentric circle.

Tangent: – A line that meets a circle exactly at one is tangent to the circle. (CD is tangent)

Point of tangency: The point where a tangent line intersects a circle is the point of tangency.