**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.

**Question 10: In each of the following, state if the statement is true (T) or false (F):**

**(i) Every circle has a centre.**

**(ii) The centre of a circle is a point of the circle.**

**(iii) Any two radii of a circle make up a diameter.**

**(iv) Every chord of a circle is parallel to some diameter of the circle.**

**(v) A circle is symmetric about each of its diameters.**

**(vi) The diameter is twice the radius.**

**(vii) A radius is a chord of the circle.**

**(viii) Concentric circles have the same radii.**

**(ix) The nearer a chord to the centre of a circle, the longer is its length.**

**Solution 10:**

**True**

**False**

**False**

**False**

**True**

**True**

**False**

**False**

**True**

**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.