Revision Notes: Circle | Mathematics Class 9 ICSE PDF Download

Related Terms

• A circle is a locus of a point which moves in such a way that its distance from a fixed point is always constant. The fixed point is called the centre of the circle.  
• The line segment joining any two points on a circle is called a chord of the circle.  
• A chord of a circle passing through its centre is called a diameter of the circle.  
  It is the largest chord of a circle.  
  Also, Diameter = 2 x Radius 
• A circle divides the plane region into three parts: 
  Circumference: A point P lies on the circle if and only if its distance from the centre of the circle is equal to the radius of the circle. 
  Interior of a circle: A point P lies inside a circle if and only if its distance from the centre of the circle is less than the radius of the circle. 
  Exterior of a circle: A point P lies outside a circle if and only if its distance from the centre of the circle is greater than the radius of the circle. 
• Circles having the same centre but with different radii are said to be concentric circles.
• Two circles are said to be equal or congruent if they have equal radii.
• A circle passing through all the vertices of a polygon is called circumscribed circle of the polygon and its centre is called circumcentre.  
  The polygon is called inscribed polygon.  
• A circle touching all the sides of a polygon is called an inscribed circle of the polygon and its centre is called incentre.

Arc, Segment and Sector

• An arc is a part of the circumference of a circle. 
• An arc less than one-half of the whole arc of a circle is called a minor arc of the circle, and an arc greater than one-half of the whole arc of a circle is called a major arc of the circle. 
  

Segment 

• A chord of a circle divides it into two parts. Each part is called a segment. 
• The part containing the minor arc is called the minor segment, and the part containing the major arc is called the major segment. 
  

Sector

• The region bounded by an arc and two radii, joining the centre to the end points of the arc, is called a sector. 
  
• The region bounded by an arc APB and radii OA and OB is a sector. 

Chord Properties 

• A straight line drawn from the centre of a circle to bisect a chord which is not a diameter is at right angles to chord. 
• Perpendicular drawn to a chord from the centre of a circle bisects the chord. 
• Equal chords of a circle are equidistant from centre. 
• Chords which are equidistant from the centre are equal in lengths. 
• There is one and only circle which passes through three given points not in a straight line. 
• The perpendicular bisector of a chord of a circle always passes through its centre. 
• Perpendicular bisectors of two chords of a circle intersect at its centre. 

Arc Properties 

• In equal circles, if two arcs subtend equal angles at the centre then they are equal. 
• In equal circles, if two arcs are equal then they subtend equal angles at the centre.  
• In equal circles, equal chords cut off equal arcs. 
• In equal circles, if two arcs are equal then their chords are equal. 
• Equal chords of the same circle subtend equal angles at the centre of the circle.
• Equal angles at the centre make equal chords. 
• Equal arcs of the same circle subtend equal angles at any point on the remaining part of the circle.