Selina Concise Mathematics Class 9 ICSE Solutions Circle

Selina Concise Mathematics Class 9 ICSE Solutions Circle

ICSE SolutionsSelina ICSE Solutions

APlusTopper.com provides step by step solutions for Selina Concise Mathematics Class 9 ICSE Solutions Chapter 17 Circle. You can download the Selina Concise Mathematics ICSE Solutions for Class 9 with Free PDF download option. Selina Publishers Concise Mathematics for Class 9 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

Download Formulae Handbook For ICSE Class 9 and 10

Selina ICSE Solutions for Class 9 Maths Chapter 17 Circle

Exercise 17(A)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 1

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 2

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 3

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 4

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 5

Solution 6:
Let O be the centre of the circle and AB and CD be the two parallel chords of length 30 cm and 16 cm respectively.
Drop OE and OF perpendicular on AB and CD from the centre O.
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 6

Solution 7:
Since the distance between the chords is greater than the radius of the circle (15 cm), so the chords will be on the opposite sides of the centre.
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 7

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 8

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 9

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 10

Exercise 17(B)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 11

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 12

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 13

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 14

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 15

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 16

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 17

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 18

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 19

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 20

Exercise 17(C)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 21

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 22
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 23

Solution 3:
As given that AB is the side of a pentagon the angle subtended by each arm of the pentagon at
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 24

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 25
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 26

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 27

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 28

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 29

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 30

Exercise 17(D)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 31

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 32

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 33

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 34

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 35

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 36

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 37

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 38

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 39

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Circle image - 40

More Resources for Selina Concise Class 9 ICSE Solutions

ICSE Solutions for Class 10 Mathematics – Circle Constructions

ICSE Solutions for Class 10 Mathematics – Circle Constructions

ICSE SolutionsSelina ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 16 Constructions (Circle) for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

Download Formulae Handbook For ICSE Class 9 and 10

Figure Based Questions

Question 1. Take a point O on the plane at the paper. With O as centre draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
Solution: Steps of construction:
(i) Take a point O on the plane at the paper and draw a circle at radius 3 cm.
circle-constructions-icse-solutions-class-10-mathematics-1

Question 2. Four equal circles, each of radius 5 cm, touch each other as shown in the figure. Find the area included between them. (Take π= 3.14)
circle-constructions-icse-solutions-class-10-mathematics-2

Question 3. In the figure alongside, OAB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded 22 portion.
circle-constructions-icse-solutions-class-10-mathematics-3

Question 4. AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm2 calculate:
circle-constructions-icse-solutions-class-10-mathematics-4

Question 5. The diagram represents the area swept by wiper of a car. With the dimension given in figure, calculate the shaded swept by the wiper.
circle-constructions-icse-solutions-class-10-mathematics-5

Question 6. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take π = 3.14).
circle-constructions-icse-solutions-class-10-mathematics-6
circle-constructions-icse-solutions-class-10-mathematics-7

Question 7. Draw a circle at radius 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.
circle-constructions-icse-solutions-class-10-mathematics-8
circle-constructions-icse-solutions-class-10-mathematics-9

Question 8. Draw a circle at radius 3 cm. Take a point at 5.5 cm from the centre at the circle. From point P, draw two tangent to the circle.
circle-constructions-icse-solutions-class-10-mathematics-10
circle-constructions-icse-solutions-class-10-mathematics-11

Question 9. Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60° and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.
circle-constructions-icse-solutions-class-10-mathematics-12

Question 10. Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
circle-constructions-icse-solutions-class-10-mathematics-13

Question 11. Draw two lines AB, AC so that ∠ B AC = 40°:
(i) Construct the locus of the centre of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose centre lies within the ∠BAC.
circle-constructions-icse-solutions-class-10-mathematics-14

Question 12. Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.
circle-constructions-icse-solutions-class-10-mathematics-15

Question 13. Construct a triangle ABC, given that the radius of the circumcircle of triangle ABC is 3.5 cm, ∠ BCA = 45° and ∠ BAC = 60°.
Solution: Steps of construction:
circle-constructions-icse-solutions-class-10-mathematics-16

Question 14. Construct an angle PQR = 45°. Mark a point S on QR such that QS = 4.5 cm. Construct a circle to touch PQ at Q and also to pass through S.
circle-constructions-icse-solutions-class-10-mathematics-17

Question 15. Construct the circumcircle of the ABC when BC = 6 cm, B = 55° and C = 70°.
circle-constructions-icse-solutions-class-10-mathematics-18
circle-constructions-icse-solutions-class-10-mathematics-19

Question 16. Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75° and the radius of the circumcircle of triangle ABC is 3.5 cm.
On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.
circle-constructions-icse-solutions-class-10-mathematics-20

Question 17. (a) Only ruler and compass may be used in this question. All contraction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.
(i) Construct a ABC, such that AB = AC = 7 cm and BC = 5 cm.
(ii) Construct AD, the perpendicular bisector of BC.
(iii) Draw a circle with centre A and radius 3 cm. Let this drcle cut AD at P.
(iv) Construct another circle, to touch the circle with centre A, externally at P, and pass through B and C.
circle-constructions-icse-solutions-class-10-mathematics-21
circle-constructions-icse-solutions-class-10-mathematics-22

Question 18. Using ruler and compass construct a cyclic quadrilateral ABCD in which AC = 4 cm, ∠ ABC = 60°, AB 1.5 cm and AD = 2 cm. Also write the steps of construction.
circle-constructions-icse-solutions-class-10-mathematics-23

Question 19. Construct a triangle whose sides are 4.4 cm, 5.2 cm and 7.1 cm. Construct its circumcircle. Write also the steps of construction.
Solution: Steps of construction:
circle-constructions-icse-solutions-class-10-mathematics-24

Question 20. Draw a circle of radius 3 cm. Construct a square about the circle.
circle-constructions-icse-solutions-class-10-mathematics-25

Question 21. Draw a circle of radius 2.5 cm and circumscribe a regular hexagon about it.
circle-constructions-icse-solutions-class-10-mathematics-26
circle-constructions-icse-solutions-class-10-mathematics-27

Question 22. Construct the rhombus ABCD whose diagonals AC and BD are of lengths 8 cm and 6 cm respectively. Construct the inscribed circle of the rhombus. Measure its radius.
circle-constructions-icse-solutions-class-10-mathematics-28

Question 23. Draw an isosceles triangle with sides 6 cm, 4 cm and 6 cm. Construct the in circle of the triangle. Also write the steps of construction.
circle-constructions-icse-solutions-class-10-mathematics-29
circle-constructions-icse-solutions-class-10-mathematics-30

Question 24. Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.
circle-constructions-icse-solutions-class-10-mathematics-31

Question 25. Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
circle-constructions-icse-solutions-class-10-mathematics-32

Question 26. Draw a circle of radius 4 cm. Take a point P out side the circle without using the centre at the circle. Draw two tangent to the circle from point P.
Solution: Steps of construction:
(i) Draw a circle of radius 4 cm.
circle-constructions-icse-solutions-class-10-mathematics-33

circle-constructions-icse-solutions-class-10-mathematics-34
circle-constructions-icse-solutions-class-10-mathematics-35

Question 28. Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with centre A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.
circle-constructions-icse-solutions-class-10-mathematics-36

circle-constructions-icse-solutions-class-10-mathematics-37
circle-constructions-icse-solutions-class-10-mathematics-38

Question 30. The centre O of a circle of a radius 1.3 cm is at a distance of 3.8 cm from a given straight line AB. Draw a circle to touch the given straight line AB at a point P so that OP = 4.7 cm and to touch the given circle externally.
circle-constructions-icse-solutions-class-10-mathematics-39

Question 31. Construct a triangle having base 6 cm, vertical angle 60° and median through the vertex is 4 cm.
circle-constructions-icse-solutions-class-10-mathematics-40
circle-constructions-icse-solutions-class-10-mathematics-41

Question 32. Using a ruler and compasses only:
(i) Construct a triangle ABC with the following data:
AB = 3.5 cm, BC = 6 cm and ∠ ABC = 120°.
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠ BCP.
circle-constructions-icse-solutions-class-10-mathematics-42
circle-constructions-icse-solutions-class-10-mathematics-43

Question 33. Draw a circle of radius 3 cm and construct a tangent to it from an external point without using the centre.
circle-constructions-icse-solutions-class-10-mathematics-44

Question 34. Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠BAC = 45° and median through the vertex A is 3.5 cm. Write also the steps of construction.
circle-constructions-icse-solutions-class-10-mathematics-45
circle-constructions-icse-solutions-class-10-mathematics-46

For More Resources

How do you Draw a Circle With a Radius of 3.5cm

CONSTRUCTION OF A CIRCLE

A circle is the path covered by a point which moves in such a way that its distance from a fixed point always remains constant. The fixed point is called the centre and the constant distance is called the radius of the circle. Hence, a circle can be drawn if its centre and radius are known.

Construction: Draw a circle of radius 3.5 cm.

  • Step 1: Mark a point O on a sheet of paper, where a circle is to be drawn.
  • Step 2: Take a pair of compasses and measure 3.5 cm using a scale.
    How do you Draw a Circle With a Radius of 3.5cm 2
  • Step 3: Without disturbing the opening of the compasses, keep the needle at mark O and draw a complete arc holding the compasses from its knob.
    After completing one complete round, we get the desired circle.
    How do you Draw a Circle With a Radius of 3.5cm 1

Read More:

What are the Parts of a Circle

What are the Parts of a Circle

So far, we have discussed about the triangle and quadrilateral that have linear boundaries. Circle is a closed figure that has a curvilinear boundary.
What are the Parts of a Circle 1When we think of circles, the very first thing that comes to our mind is its round shape, for example, bangles, coins, rings, plates, chapattis, pizzas, CDs etc. Wheels of a car, bus, cycle, truck, train, and aeroplane are also round in shape. If we take a stone, tie it to one end of a string and swing it in the air by holding the other end of the string, the path traced by the stone will be a circular path and it will make a circle.

Read More:

  1. Circle: A circle is a collection of all those points in a plane that are at a given constant distance from a given fixed point in the plane.
  2. Centre: Circle is a closed figure made up of points in a plane that are at the same distance from a fixed point, called the centre of the circle. In the figure O is the centre.
    What are the Parts of a Circle 3

 

  1. Radius: The constant distance from its centre is called the radius of the circle. In the figure, OA is radius
    What are the Parts of a Circle 2
  2. Chord: A line segment joining two points on a circle is called a chord of the circle. In the figure, AB is a chord of the circle. If a chord passes through centre then it is longest chord. PQ, PR, and ST are chords of the circle. Chord ST passes through the centre, hence it is a diameter.
    What are the Parts of a Circle 4
  3. Diameter: A chord passing through the centre of a circle is called the diameter of the circle. A circle has an infinite number of diameters. CD is the diameter of the circle as shown in the figure. If d is the diameter of the circle then d = 2r. where r is the radius. or the longest chord is called diameter.
    In the figure, AB is the diameter and the arcs CD and DC are semicircles.
    What are the Parts of a Circle 5
  4. Arc: A continuous piece of a circle is called an arc. Let A,B,C,D,E,F be the points on the circle. The circle is divided into different pieces. Then, the pieces AB, BC, CD, DE, EF etc. are all arcs of the circle.
    What are the Parts of a Circle 6Let P,Q be two points on the circle. These P, Q divide the circle into two parts. Each part is an arc. These arcs are denoted in anti-clockwise direction
    arc
  5. Circumference of a circle: The perimeter of a circle is called its circumference. The circumference of a circle of radius r is 2πr.
  6. Semicircle: The diameter of a circle divides the circle into two equal parts. Each part is called a semi-circle. We can also say that half of a circle is called a semi¬circle. In the figure,  AXB and AYB represents two semi-circles.
  7. Segment: Let AB be a chord of the circle. Then, AB divides the region enclosed by the circle (i.e., the circular disc) into two parts. Each of the parts is called a segment of the circle. The segment, containing the minor arc is called minor segment and the segment, containing the major arc, is called the major segment and segment of a circle is the region between an arc and chord of the circle.
    What are the Parts of a Circle 7
  8. Central Angles: Consider a circle. The angle subtended by an arc at the centre O is called the central angle. The vertex of the central angle is always at the centre O.
    What are the Parts of a Circle 8
  9. Degree measure of an arc: Degree measure of a minor arc is the measure of the central angle subtended by the arc.
    arc-1
    The degree measure of the circumference of the circle is always 360°.
  10. Interior and Exterior of Circle
    A circle divides the plane on which lies into three parts.
    (i) Inside the circle. which is called the interior of the circle
    (ii) Circle
    (iii) Outside the circle, which is called the exterior of the circle.
    The circle and its interior make up the circular region.
    What are the Parts of a Circle 9
  11. Sector:
    A sector is that region of a circular disc which lies between an arc and the two radii joining the extremities of the arc and the centre. OAB is a sector as shown in the figure.
    Quadrant: One fourth of a circular disc is called a quadrant.
    What are the Parts of a Circle 10
  12. Position of a point:
    Point Inside the circle: A point P, such that OP < r, is said to lie inside the circle.
    What are the Parts of a Circle 11The point inside the circle is also called interior point. (Example : Centre of cirle)
    Point outside the circle: A point Q, such that OQ > r, is said to lie outside the circle C (O, r) = {X, OX = r}
    The point outside the circle is also called exterior point.
    Point on the circle: A point S, such that OS = r is said to lie on the circle C(O, r) = {X ,OX = r}.
    Circular Disc: It is defined as a set of interior points and points on the circle. In set notation, it is written as : C(O, r) = {X : P OX ≤ r}
    What are the Parts of a Circle 12
  13. Concentric Circles:
    Circles having the same centre and different radius are said to be concentric circles.
    Remark. The word ‘radius’ is used for a line segment joining the centre to any point on the circle and also for its length.
    What are the Parts of a Circle 13
  14. Congruence of Circles & Arcs
    Congruent circles: Two circles are said to be congruent if and only if, one of them can be superposed on the other, so as the cover it exactly. It means two circles are congruent if and only if, their radii are equal. i.e., C (O, r) and C (O’ , r) are congruent if only if r = s.
    What are the Parts of a Circle 14Congruent arcs: Two arcs of a circle are congruent, if either of them can be superposed on the other, so as to cover it exactly. It is only possible, if degree measure of two arcs are the same.

Example 1: Take two points A and B on a plane sheet. Draw a circle with A as a centre, AC as radius and B in its exterior.
Solution: Mark two points A and B on a paper.
A •            • B
As the point B should be in the exterior of the circle, take A as the centre and radius (r) less than AB to draw a circle.
circle

Example 2 :Find the diameter of the circle of radius 6 cm.
Solution: We know,
Diameter = 2 × radius
∴ Diameter =2 × 6 cm =12 cm