Exercise 14.1
Question 1: Explain the following:
(i) Circle
(ii) Radius
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution 1:
(i) Circle:- A circle is a simple closed curve which is not a polygon. It is a set of all those points in a plane whose distance is equal from a fixed point. For Example:- a wheel, a bangle, a coin etc.
(ii) Radius:- The distance between the all the points of the circle to its centre is called radius.
(iii) Centre:– The mid-point of a circle which is at a constant distance from all the points called centre.
(iv) Diameter:– Diameter is a line segment passing through the centre of a circle, and having its end-points on the circle.
(v) Chord:– Chord of a line segment with its end-points lying on a circle.
(vi) Interior of a circle:–
The inside plane part of a circle called the interior of a circle.
Question 2: Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same centre O.
Solution 2: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.
Question 3: Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle. Join AB, BC, CD and DA.
Solution 3:
Question 4: Draw a circle with centre O and radius 6 cm. Mark points P, Q, R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.
Rewrite each of the following statements using the correct symbol (=, < or >):
(i) OQ …… 5 cm (ii) OP ……. 5 cm (iii) OR …… 5 cm.
Solution 4:
Question 5: Take two points A and B on the page of your note book. Draw a circle with centre A which passes through B.
Solution 5:
Question 6: Draw a semi-circle with centre O and radius 5 cm. Is the diameter that determines the semi-circle, a part of the semi-circle?
Solution 6: The figure given below shows a semi-circle with centre O and radius 5 cm.
The end point of the diameter of a circle divides the circle into equal parts. The diameter does not determine the semi-circle and it is the end points of the diameter which finds the semi-circle or a part of the semi-circle.
Question 7: The diameter of a circle is 14 cm, find its radius.
Solution 7: Diameter of a circle = 14 cm
Question 8: Given a circle with centre O and radius 2.5 cm, what is the length of the longest chord of the circle.
Solution 8:
The diameter of a circle is diameter.
Diameter = 2 × Radius
Diameter = 2 × 2.5
Diameter = 5 cm
Hence, the length of the longest chord of the circle is 5cm.
Question 9: Fill in the blanks:
(i) The diameter of a circle is ___________ times its radius.
(ii) The diameter of a circle is the ___________ chord of the circle.
(iii) The diameter of a circle pass through ___________.
(iv) A chord of a circle is a line segment with its end points on the ___________
(v) If we join any two points on a circle by a line segment, we obtain ___________ of the circle.
(vi) A radius of a circle is a line segment with one end at ___________ and the other end at _________.
(vii) All radii of a circle are ___________.
(viii) The diameters of a circle are ___________.
(ix) The total number of diameters of a circle is ___________.
(x) Every point on a circle is ___________ from its centre.
(xi) A chord of a circle contains exactly ___________ points of the circle.
(xii) A diameter is the longest ___________.
(xiii) Concentric circles are circles having ___________.
Solution 9:
(i) The diameter of a circle is two times its radius.
(ii) The diameter of a circle is the longest chord of the circle.
(iii) The diameter of a circle pass through its centre.
(iv) A chord of a circle is a line segment with its end points on the circle.
(v) If we join any two points on a circle by a line segment, we obtain chord of the circle.
(vi) A radius of a circle is a line segment with one end at centre and the other end at circle.
(vii) All radii of a circle are equal.
(viii) The diameters of a circle are concurrent.
(ix) The total number of diameters of a circle is infinite.
(x) Every point on a circle is equidistant from its centre.
(xi) A chord of a circle contains exactly two points of the circle.
(xii) A diameter is the longest chord.
(xiii) Concentric circles are circles having same centre.
Objective Type Questions ::->
Mark the correct alternative in each of the following:
Question 1: A circle of radius r cm has diameter of length
(a) r cm
(b) 2r cm
(c) 4r cm
(d) r/2 cm
Solution 1: (b)
Diameter = 2 × Radius
D = 2r
Question 2: A chord of a circle passing through its centre is equal to its
(a) radius
(b) diameter
(c) circumference
(d) none of these
Solution 2: (b)
Diameter:- A chord of a circle passing through its centre.
Question 3: The total number of diameters of a circle is
(a) 1
(b) 2
(c) 4
(d) uncountable number
Solution 3: (d)
Many diameters can be formed in circle.
Question 4: By joining any two points on a circle, we obtain its
(a) radius
(b) diameter
(c) chord
(d) circumference
Solution 4: (c)
We can obtain chord by joining any two points on a circle.
Question 5: The longest chord of a circle is equal to its
(a) radius
(b) diameter
(c) circumference
(d) perimeter
Solution 5: (b)
Diameter:- The longest chord of a circle.
Question 6: How many circles can be drawn to pass through two given points?
(a) 1
(b) 2
(c) 0
(d) As many as possible
Solution 6: (d)
As many as possible circles can be drawn to pass through two given points.
Question 7: How many circles can be drawn to pass through three non-collinear points?
(a) 1
(b) 2
(c) 0
(d) As many as possible
Solution 7: (a)
By three non-collinear points we can draw only 1 circle.