How to Draw a Circle of Radius 6 Cm

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 29 The Circle

Selina Publishers Curtailed Mathematics Class vi ICSE Solutions Affiliate 29 The Circle

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IMPORTANT POINTS

1. A circumvolve is a round enclosed figure, whose mid-betoken is called its centre.

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

v. Concentric circles: Ii or more circles having the aforementioned heart but different radii are called concentric circles.
half-dozen. Chord of a circle: A line which divides the circle into two parts is called chord of the circle. Diameter is the longest chord of the circle.

seven. Segment of a circle: When a chord divides the circumvolve into ii unequal parts, the bigger part is called the major segment and smaller function is called the modest segment.
8. Arc of a circle: A part of circumference of a circumvolve is called an arc of the circle. Arc greater than one-half circle is called the major arc and less than half circle is called the modest arc.
nine. Sector of a circumvolve: A bore divides the circle into two equal parts and each function is called a semicircle. Sector greater than a semi-circumvolve is called the major sector and less than semi-circle is called the minor sector of the circle.

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

Question 1.
Use the figure given below to fill in the blanks :
(i) R is the …… of the circle.
(ii) Diameter of a circle is …… .
(3) Tangent to a circle is … .
(iv) EF is a …… of the circle.
(v) …… is a chord of the circumvolve.
(vi) Diameter = 2 x …..
(vii) ……. is a radius of the circumvolve.
(8) If the length of RS is v cm, the length of PQ = ……
(9) If PQ is eight cm long, the length of RS =…..
(x) AB is a ….. of the circumvolve

Solution:
(i) middle
(2) PQ
(iii)AB
(four) secant
(v) CD
(vi) radius
(vii) RS
(viii) x cm
(ix) 4 cm
(x) tangent.

Question 2.
Draw a circle of radius iv.two cm. Marker its centre equally O. Take a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,
(i) Measure the length of AB.
(two) Assign a special name to AB.
Solution:

(i) By measurement AB = 8.4 cm.
(ii) ∴ AB is the diameter of the circumvolve.

Question 3.
Depict circle with diameter :
(i) 6 cm
(ii) 8.4 cm.
In each case, measure out the length of the radius of the circle drawn.
Solution:

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

Question 5.
Depict a circle of radius iv.8 cm and marking its centre as P.
(i) Draw radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
Solution:

PA is the radius of circle. i.c., PA = 4.8 cm.
(i) ∠APB = 45° in which P is the heart of the circle and PA and PB are radii of circle.
(2) Major sector of circle is shaded in the figure.

Question 6.
Draw a circle of radius 3.half-dozen cm. In the circumvolve, draw a chord AB = 5 cm. Now shade the minor segment of the circumvolve.
Solution:
Shaded portion of circle is the small-scale segment of the circle.

Question vii.
Marking two points A and B ,4cm a part, Draw a circle passing through B and with A as a center

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

Question 8.
Describe 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:

Past measurement ∠ACB =90

The Circle Practice 29B – Selina Concise Mathematics Class half dozen ICSE Solutions

Question 1.
Construct a triangle ABC with AB = 4.2 cm, BC = six cm and Air-conditioning = 5cm. Construct the circumcircle of the triangle drawn.
Solution:
Steps of Construction :

(i) Depict ∆ABC in which AB = iv.ii cm. BC = 6 cm. and Ac = five cm.
(2) Draw the perpendicular bisectors of any two sides of the triangle. Permit these intersect at O.
(iii) Taking O as center and OA or OB or OC as radius draw a circle.
This circumvolve will pass through vertices A, B and C.

Question two.
Construct a triangle PQR with QR = 5.v cm, ∠Q = sixty° and bending R = 45°.
Construct the circumcircle cif the triangle PQR.
Solution:
Steps of Construction :

(i) Draw a ∆PQR in which QR = 5.five cm, ∠Q = sixty° and ∠R = 45°.
(ii) Depict the arc bisector of PQ and PR which intersect at O.
(iii) Taking O every bit centre and radius OP or OQ or OR describe a circle.
This circle volition pass through vertices P, Q and R.

Question three.
Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = six. 4 cm.
Depict the incircle of the triangle ABC. Sol. Steps of Construction :
Solution:
Steps of Construction:

(i) Describe a line AB = 5 cm.
(ii)B as a centre draw an bending with the help of compass ∠B = 60°. Cut the line with an arc BC = 6 four cm.
(three) Join Air-conditioning.
(iv) Now, from A and B cut the bisector of ∠A and ∠B, which intersect each other at signal D.
(5) With D as a heart draw an incircle which touches all the 3 sides of AABC.

Question iv.
Construct a triangle XYZ in which XY = YZ= 4.5 cm and ZX = five.4 cm. Draw the circumcircle of the triangle and measure its circumradius.
Solution:
Steps of Construction :

(i) Depict a triangle XYZ in which XY = YZ = 4.v cm and ZX = 5.four cm.
(two) Depict the bisectors of XZ and YZ which meet at O.
(iii) With O as centre and radius OX or OY or OZ draw a circle.
This circle volition laissez passer through X, Y and Z.

Question v.
Construct a triangle PQR in which, PQ = QR = RP = 5.seven cm. Describe the incircle of the triangle and mensurate its radius.
Solution:
Steps of Structure :

(i) Describe an equilateral ∆ RPQ in which PQ = QR = RP = 5.7 cm each.
(ii) From P and Q cut the bisector of ∠P and ∠Q, which intersect each other at signal O.
(iii) With P as a centre depict an incircle which touches all the three sides of ∆RPQ.

The Circumvolve Revision Do – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The middle of a circle is at bespeak O and its radius is 8 cm. State the position of a point P (signal P may lie within the circle, on the circumference of the circumvolve, or outside the circumvolve), when :
(a) OP = x.6 cm
(b) OP = six.viii cm
(c) OP = 8 cm
Solution:
(a) Draw circle each of radius viii cm. With centre O
In figure (i) draw OP = 10.half dozen cm

We see that point P lies outside the circumvolve as OP > radius of the circle
(b) In effigy (two) OP = 6.8 cm. We run into that P lies within the circle as OP < radius of the circle.
(c) In effigy, OP = 8 cm. We see that P lies on the circle as OP = radius of the circle.

Question 2.
The diameter of a circle is 12.vi cm. Country, the length of its radius.
Solution:
Bore of the circle = 12.6 cm
∴Radius = \(\frac { i }{ two }\) diameter = \(\frac { 1 }{ ii }\) 10 12.6 cm
= half dozen.3 cm

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

Question four.
Depict a circumvolve of diameter 7 cm. Draw 2 radii of this circumvolve such that the angle between these radii is 90°. Shade the small-scale sector obtained. Write a special name for this sector.
Solution:
Draw a circumvolve with bore = vii cm
OA and OB are the radii of the circle such that ∠AOB = 90°
Now shade the modest sector AOB This is the quadrant of the circle

Question five.
State, which of post-obit statements are truthful and which are false :
(i) If the end points A and B of the line segment lie on the circumference of a circle, AB is a bore.
(two) The longest chord of a circumvolve is its diameter.
(3) Every diameter bisects a circumvolve and each part of the circle and then obtained is a semi-circle.
(iv) The diameters of a circle always pass through the same signal in the circumvolve.
Solution:
(i) Faux, as AB may exist diameter or may not be, it can be chord.
(two) True, diameter of a circumvolve is the longest chord.
(iii) True.
(iv) True, all the diameter of a circle pass through the aforementioned point i.e., centre, of the circle.

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