# Circles

Notes of chapter: Circles are presented below. Indepth notes along with worksheets and NCERT Solutions of class 9.

(1) Circle-

A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.

Figure of circle is showing below-

O is a fixed point.

Parts of the circle-

(i) Center-

The fixed point of circle is known as center.

Eg:- O is center of the circle.

The distant from center of the circle to the boundary of circle is known as radius.

Eg:- OP is distance from center and boundary of the circle.

(iii) Chord-

The line segments which touches boundary of the circle is known as chord.

Eg:- AB is a chord of the circle.

(a) Diameter-

The chord which passes from the center is known as diameter.

Eg:- CD is a diameter of the circle.

Properties of the diameter-

(A) It is longest chord of the circle.

(B) All diameters of a circle are equal in lengths.

(C) Diameter is twice of the radius of the circle.

(iv)The part of a circle between two points is called an arc.

Eg:- In figure below, points P and Q divides circle in two parts which are known as arcs. One arc is PAQ and second arc is PBQ.

Types of arcs-

(a) Major arc –

The longer part of a circle between two points on a circle is known as major arc.

Eg:- In figure below, PRQ is a major arc.

(b) Minor arc-

The shorter part of a circle between two points on a circle is known as minor arc.

Eg:- In figure below PQ is a minor arc.

(c)Semicircle-

When P and Q are ends of a diameter then both arcs are equal and called as semicircle.

Eg:- In figure below P and Q are ends of diameter PQ. Therefore, PRQ and PSQ are equal and semicircle.

(vi) Segment-

The region between the chord and the arc is called as segment of the circle.

Eg:- In figure below, circle has two segments.

Types of the segments –

(a) Major segment-

The region between the chord and the large arc is called as major segment of the circle.

Eg:- In figure below PRQ is a major segment.

(b) Minor segment-

The region between the chord and the small arc is called as minor segment of the circle.

Eg:- In figure below PSQ is a minor segment.

(vii)Sector-

The region between an arc and two radii is known as sector of a circle.

Eg:- In figure below, circle has two sectors.

Types of sector-

(a) Major sector-

The region between major arc and two radii is known as major sector of a circle.

Eg:- In figure below, circle has major sector.

(b)Minor sector-

The region between minor arc and two radii is known as minor sector of a circle.

Eg:- In figure below, circle has minor sector.

(2) A circle divides a plane on which it lies into three parts.

(i)The region of plane inside of the circle is known as interior of the circle.

Eg:- In figure below, interior of the circle is presented.

(ii)The region of plane outside of the circle is known as exterior of the circle.

Eg:- In figure below, exterior of the circle is presented.

(iii)The boundary of the circle is known as circle.

Eg:- In figure below, circle is presented.

The circle and its interior make up the circular region.

Take three non – collinear points A, B and C.

Draw perpendicular bisectors PQ and RS of AB and BC respectively.

Let these perpendiculars bisectors intersect at point O. ( Two lines intersect only at one point.)

Point O lies on the perpendicular bisector PQ of AB,

OA = OB …(1)

(Every point of perpendicular PQ is equidistance from end points of AB)

Similarly, point O lies on the perpendicular bisector RS of BC,

OB = OC (  every point of perpendicular PQ is equidistance from end points of AB)…(2)

OA = OB = OC (From equation 1 and 2)

Therefore, we can draw a circle with centre O which will pass through point A, B and C.

Hence, proved.

Reflex angle

Helping Topics

NCERT Solutions Class 9

Worksheet Class 9