Draw a Circle of Radius 4.8 Cm

Selina Concise Mathematics Class vi ICSE Solutions Chapter 29 The Circle

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

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IMPORTANT POINTS

1. A circle is a circular enclosed figure, whose mid-point is chosen its eye.

2. The line segment joining the centre to any point on the circumvolve is called a radius. A heart has infinite radii and all radii of a circle are equal.
3. A line segment which contains the centre of the circle and whose ends points lie on the circle is chosen diameter of the circle. Diameters of a circle are also equal.
4. Parts of a circle: A circumvolve has 3 parts (i) Interior (ii) Exterior and (three) Circle itself.

5. Concentric circles: Ii or more circles having the same middle simply dissimilar radii are chosen concentric circles.
vi. Chord of a circle: A line which divides the circle into 2 parts is chosen chord of the circle. Diameter is the longest chord of the circle.

7. Segment of a circle: When a chord divides the circumvolve into two unequal parts, the bigger part is called the major segment and smaller part is chosen the minor segment.
8. Arc of a circumvolve: A role of circumference of a circle is called an arc of the circumvolve. Arc greater than half circumvolve is called the major arc and less than half circumvolve is called the minor arc.
9. Sector of a circle: A diameter divides the circumvolve into two equal parts and each part is called a semicircle. Sector greater than a semi-circle is called the major sector and less than semi-circle is called the minor sector of the circle.

The Circle Practise 29A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Use the effigy given below to fill up in the blanks :
(i) R is the …… of the circle.
(ii) Diameter of a circle is …… .
(iii) Tangent to a circle is … .
(four) EF is a …… of the circle.
(v) …… is a chord of the circle.
(vi) Bore = 2 x …..
(seven) ……. is a radius of the circumvolve.
(8) If the length of RS is five cm, the length of PQ = ……
(9) If PQ is 8 cm long, the length of RS =…..
(x) AB is a ….. of the circle

Solution:
(i) heart
(ii) PQ
(three)AB
(iv) secant
(v) CD
(half dozen) radius
(7) RS
(viii) ten cm
(ix) 4 cm
(x) tangent.

Question 2.
Draw a circle of radius iv.2 cm. Mark its heart every bit O. Take a indicate A on the circumference of the circle. Bring together AO and extend it till information technology meets indicate B on the circumference of the circumvolve,
(i) Measure the length of AB.
(ii) Assign a special name to AB.
Solution:

(i) By measurement AB = viii.4 cm.
(ii) ∴ AB is the diameter of the circle.

Question 3.
Draw circumvolve with diameter :
(i) half-dozen cm
(ii) 8.4 cm.
In each case, measure the length of the radius of the circle drawn.
Solution:

Question four.
Draw a circle of radius 6 cm. In the circle, draw a chord AB = half dozen cm.
(i) If O is the centre of the circle, join OA and OB.
(ii) Assign a special proper name to ∆AOB
(iii) Write the measure out of bending AOB.
Solution:

Question v.
Draw a circumvolve of radius 4.8 cm and mark its centre equally P.
(i) Depict radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
Solution:

PA is the radius of circumvolve. i.c., PA = four.eight cm.
(i) ∠APB = 45° in which P is the centre of the circle and PA and PB are radii of circle.
(ii) Major sector of circle is shaded in the figure.

Question 6.
Draw a circle of radius 3.6 cm. In the circle, draw a chord AB = 5 cm. Now shade the minor segment of the circle.
Solution:
Shaded portion of circumvolve is the minor segment of the circle.

Question seven.
Mark two points A and B ,4cm a part, Describe a circumvolve passing through B and with A as a center

Solution:
In the figure, A is the center of the circumvolve and AB = 4 cm [radius of circle]

Question 8.
Draw a line AB = 8.4 cm. Now draw a circle with AB as diameter. Mark a point C on the circumference of the circle. Measure angle ACB.
Solution:

By measurement ∠ACB =xc

The Circle Exercise 29B – Selina Concise Mathematics Form 6 ICSE Solutions

Question ane.
Construct a triangle ABC with AB = 4.ii cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle fatigued.
Solution:
Steps of Structure :

(i) Depict ∆ABC in which AB = 4.2 cm. BC = 6 cm. and Air-conditioning = v cm.
(ii) Draw the perpendicular bisectors of any ii sides of the triangle. Allow these intersect at O.
(iii) Taking O as centre and OA or OB or OC as radius describe a circle.
This circle will pass through vertices A, B and C.

Question 2.
Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and bending R = 45°.
Construct the circumcircle cif the triangle PQR.
Solution:
Steps of Construction :

(i) Draw a ∆PQR in which QR = 5.5 cm, ∠Q = 60° and ∠R = 45°.
(ii) Draw the arc bisector of PQ and PR which intersect at O.
(iii) Taking O equally centre and radius OP or OQ or OR depict a circle.
This circle will pass through vertices P, Q and R.

Question 3.
Construct a triangle ABC with AB = v cm, ∠B = 60° and BC = 6. 4 cm.
Draw the incircle of the triangle ABC. Sol. Steps of Construction :
Solution:
Steps of Construction:

(i) Draw a line AB = v cm.
(ii)B as a middle describe an angle with the help of compass ∠B = 60°. Cut the line with an arc BC = 6 four cm.
(iii) Join AC.
(iv) Now, from A and B cutting the bisector of ∠A and ∠B, which intersect each other at signal D.
(v) With D as a centre draw an incircle which touches all the three sides of AABC.

Question iv.
Construct a triangle XYZ in which XY = YZ= 4.5 cm and ZX = 5.four cm. Draw the circumcircle of the triangle and measure out its circumradius.
Solution:
Steps of Construction :

(i) Describe a triangle XYZ in which XY = YZ = 4.5 cm and ZX = 5.four cm.
(ii) Draw the bisectors of XZ and YZ which meet at O.
(3) With O as middle and radius OX or OY or OZ draw a circle.
This circumvolve will pass through X, Y and Z.

Question 5.
Construct a triangle PQR in which, PQ = QR = RP = 5.7 cm. Draw the incircle of the triangle and measure its radius.
Solution:
Steps of Structure :

(i) Describe an equilateral ∆ RPQ in which PQ = QR = RP = v.7 cm each.
(ii) From P and Q cut the bisector of ∠P and ∠Q, which intersect each other at bespeak O.
(iii) With P equally a heart depict an incircle which touches all the 3 sides of ∆RPQ.

The Circle Revision Exercise – Selina Concise Mathematics Grade 6 ICSE Solutions

Question 1.
The centre of a circumvolve is at bespeak O and its radius is 8 cm. State the position of a signal P (indicate P may lie inside the circumvolve, on the circumference of the circle, or outside the circle), when :
(a) OP = 10.half dozen cm
(b) OP = 6.8 cm
(c) OP = 8 cm
Solution:
(a) Describe circle each of radius eight cm. With centre O
In figure (i) draw OP = ten.6 cm

We see that point P lies outside the circumvolve as OP > radius of the circle
(b) In figure (ii) OP = vi.viii cm. Nosotros see that P lies inside the circle as OP < radius of the circle.
(c) In figure, OP = 8 cm. We come across that P lies on the circle as OP = radius of the circle.

Question 2.
The diameter of a circle is 12.half-dozen cm. Land, the length of its radius.
Solution:
Diameter of the circumvolve = 12.6 cm
∴Radius = \(\frac { 1 }{ 2 }\) diameter = \(\frac { i }{ 2 }\) 10 12.6 cm
= 6.3 cm

Question 3.
Can the length of a chord of a circumvolve be greater than its diameter ? Explain.
Solution:
No, the length of chord cannot exist greater than the diameter of the cirlce every bit the diameter of a circumvolve is the greatest chord of that circle.

Question 4.
Draw a circumvolve of bore vii cm. Describe two radii of this circle such that the bending between these radii is xc°. Shade the minor sector obtained. Write a special name for this sector.
Solution:
Draw a circumvolve with diameter = vii cm
OA and OB are the radii of the circle such that ∠AOB = 90°
At present shade the minor sector AOB This is the quadrant of the circle

Question 5.
State, which of post-obit statements are true and which are false :
(i) If the end points A and B of the line segment prevarication on the circumference of a circumvolve, AB is a diameter.
(ii) The longest chord of a circle is its diameter.
(three) Every diameter bisects a circle and each part of the circle so obtained is a semi-circle.
(iv) The diameters of a circle always laissez passer through the same point in the circle.
Solution:
(i) False, every bit AB may be diameter or may not exist, information technology can be chord.
(ii) True, bore of a circle is the longest chord.
(iii) True.
(iv) Truthful, all the diameter of a circle laissez passer through the same point i.east., centre, of the circle.

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