Circle Class-8 RS Aggarwal ICSE Maths Goyal Brothers
Circle Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-21. We provide step by step Solutions of Exercise / lesson-21 Circle for ICSE Class-8 RS Aggarwal Mathematics.
Our Solutions contain all type Questions of Exe-21 with Notes to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.
Circle Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-21
-: Select Topic :-
Notes on Circle
. A circle is the locus of the points drawn at an equidistant from the centre. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
A circle is a basic 2D shape which is measured in terms of its radius. The circles divide the plane into two regions such as interior and exterior regions
Circle Definition
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry.
- Arc – It is basically the connected curve of a circle
- Sector – A region bounded by two radii and an arc.
- Segment- A region bounded by a chord and an arc lying between the chord’s endpoints. It is to be noted that segments do not contain the centre
- Centre – It is the midpoint of a circle.
- Chord- A line segment whose endpoints lie on the circle
- Diameter- A line segment having both the endpoints on the circle
- Radius- A line segment connecting the centre of a circle to any point on the circle itself.
- Secant- A straight line cutting the circle at two points. It is also called as an extended chord.
- Tangent- A coplanar straight line touching the circle at a single point.
Radius of Circle (r)
A line segment connecting the centre of a circle to any point on the circle itself “. The radius of the circle is denoted by “R” or “r”
Diameter (d) of Circle
A line segment having both the endpoints on the circle. It is twice the length of radius i.e. d = 2r. From the diameter, the radius of the circle formula is obtained as r= d/2
Circle Formulas
Circumference (C) | The circumference of a circle is defined as the distance around the circle. The word ‘perimeter’
is also sometimes used, although this usually refers to the distance around polygons, figures made up of the straight line segment. A circle circumference formula is given by C = πd = 2 π r Where, π = 3.1415 |
Area (A) |
The Area of a circle is the amount of space occupied by the circle. The circle formula to find the area is given by Formulas for Area of a circle = πr^{2} |
Properties of Circles
Here are some basic properties of circles.
- The outer line of a circle is at equidistant from the center.
- The diameter of the circle divides it into two equal parts
- Circles which have equal radii are congruent to each other.
- Circles which are different in size or having different radii are similar.
- The diameter of the circle is the largest chord and is double of the radius.
EXE-21 , Circle Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Solutions Chapter-21
Question 1:
Take a point O on your notebook and draw circles of radii 3.6 cm, 4.5 cm and 5.3 cm, each having the same centre O.
Answer :
Construction :
(i) Take a point O
(ii) With centre O and radius 3.6 cm, draw a circle
(iii) With centre O and radius 4.5 cm, draw another circle
(iv) Similarly with centre O and radius 5.3 cm, draw a third circle.
These are the required circles.
Question 2:
Draw a circle with centre C and radius 4.2 cm. Mark points, P, Q, R such that P lies in the interior of the circle, Q lies on the circle and R lies in the exterior of the circle.
Answer :
Construction :
(i) Take a point C.
(ii) With centre C and radius 4.2 cm, draw n circle
(iii) Now mark points P, Q and R such that P lies in the interior, Q lies on the circle and R lies out side the circle as shown.
Question 3:
Draw a circle with centre O and radius 4.5 cm. Draw a chord AB of lengths 5.4 cm. Indicate by marking points X and Y, the minor arc AXB and the major arc AYB of the circle. Shade the major segment of the circle AB.
Answer :
Construction :
(i) Take a point O
(ii) With centre O and radius 4.5 cm, draw a circle.
(iii) Draw a chord AB 5.4 cm.
(iv) This chord divides circle into two segments.
(v) Mark point X and Y in such a way.
That AXB is a minor segment and AYB is major segment.
Now shade the major segment AYB as shown.
Question 4:
Draw a circle with centre O and radius 3.6 cm. Draw a sector OAXB having the angle 75°. Measure the length of chord AB.
Answer :
Construction:
(i) Take a point O.
(ii) With centre O and radius 3.6 cm, draw a circle.
(iii) At O, draw a ray making an angle of 75° which marks the Circle at B and mark a point X on arc AB.
(v) Join AB
On measuring AB 4.5 cm (approx.)
Question 5:
State which of the following statements are true and which are false:
(i) Every circle has a unique centre.
(ii) Each radius of a circle IS also a chord of the circle.
(iii) Every circle has a unique diameter.
(iv) A line can meet a circle at the most at two points.
(v) A circle consists of an infinite number of points.
(vi) A secant of a circle is a segment having its end points on the circle.
(vii) One and only one tangent can be drawn to pass through a point on the circle.
(viii) One and only one tangent can be drawn to a circle from a point outside it.
(ix) An infinite number of chords can be drawn inside a circle.
(x) A minor arc is bigger than a semi-circle.
Answer :
(i) True: A circle has a unique centre.
(ii) False: Radius is not a chord as chord meets the circles at two points.
(iii) False: As a circle as infinite number of diameters.
(iv) True : A lines meets the circle not more than two points.
(v) True : A circle has infinite number of points.
(vi) False: A secant of a circle is a line which intersects it at two points.
(vii) True: One and only one tangent can be drawn to a circle through a point on it.
(viii) False: From a point outside a circle, two tangent can be drawn to the circle.
(ix) True
(x) False : A major arc is bigger than semi circle.
Question 6:
Fill in the blanks :
(i) …………………….. is the longest chord of a circle.
(ii) Every point on a circle is ……………….. from its centre.
(iii) The perimeter of a circle is called its ………………..
(iv) A part of a circle bounded by an ……………… and a …………….. is Called a segment.
(v) A part of a circle bounded by an ………………….. and the two ………………… at its ends is called a sector.
(vi) A …………………….. of a circle divides the circular region into two parts each called a segment.
Answer :
(i) Diameter is the longest chord of a circle.
(ii) Every point on a circle is equidistant from its centre.
(iii) The perimeter of a circle is called its circumference.
(iv) A part of a circle bounded by an arc and a chord is Called a segment.
(v) A part of a circle bounded by an arc and the two radii at its ends is called a sector.
(vi) A chord of a circle divides the circular region into two parts each called a segment.
Question 7:
In the adjoining figure, name:
(i) all the radii
(ii) all the diameters
(iii) all the chords
(iv) a minor arc
(v) a major are
(vi) a minor segment
(vii) a major segment
(viii) a minor sector
(ix) a major sector
Answer :
(i) OA, OB, OC, OF
(ii) AB
(iii) AB, CD, DE
(iv) ◠AFD
(v) ◠CBD
(vi) CADC
(vii) CBDC
(viii) OCAFO
(ix) OCBFO
–: End of Circle Class-8 RS Aggarwal Solutions :–
Return to- RS Aggarwal Solutions for ICSE Class-8 Goyal Brothers Prakashan
Thanks