Page 1 1. Explain the following: (i) Circle (ii) Radius (iii) Centre (iv) Diameter (v) Chord (vi) Interior of a circle. Solution: (i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant. (ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre. (iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points. (iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle. (v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle. (vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a circle. 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: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre. 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: Page 2 1. Explain the following: (i) Circle (ii) Radius (iii) Centre (iv) Diameter (v) Chord (vi) Interior of a circle. Solution: (i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant. (ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre. (iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points. (iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle. (v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle. (vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a circle. 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: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre. 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: The figure given below shows a circle with centre O and two perpendicular diameter AC and BD. 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: The figure given below shows the points P, Q and 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. The statements can be written as (i) OQ < 5 cm (ii) OP = 5 cm (iii) OR > 5 cm Page 3 1. Explain the following: (i) Circle (ii) Radius (iii) Centre (iv) Diameter (v) Chord (vi) Interior of a circle. Solution: (i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant. (ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre. (iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points. (iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle. (v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle. (vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a circle. 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: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre. 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: The figure given below shows a circle with centre O and two perpendicular diameter AC and BD. 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: The figure given below shows the points P, Q and 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. The statements can be written as (i) OQ < 5 cm (ii) OP = 5 cm (iii) OR > 5 cm 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: The figure given below shows the circle with A as centre and a line which passes through B. 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: The figure given below shows a semi-circle with centre O and radius 5 cm. We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts. No, 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. 7. The diameter of a circle is 14 cm, find its radius. Solution: It is given that Diameter of a circle = 14 cm We know that Radius of a circle = Diameter / 2 By substituting the values Page 4 1. Explain the following: (i) Circle (ii) Radius (iii) Centre (iv) Diameter (v) Chord (vi) Interior of a circle. Solution: (i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant. (ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre. (iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points. (iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle. (v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle. (vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a circle. 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: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre. 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: The figure given below shows a circle with centre O and two perpendicular diameter AC and BD. 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: The figure given below shows the points P, Q and 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. The statements can be written as (i) OQ < 5 cm (ii) OP = 5 cm (iii) OR > 5 cm 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: The figure given below shows the circle with A as centre and a line which passes through B. 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: The figure given below shows a semi-circle with centre O and radius 5 cm. We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts. No, 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. 7. The diameter of a circle is 14 cm, find its radius. Solution: It is given that Diameter of a circle = 14 cm We know that Radius of a circle = Diameter / 2 By substituting the values Radius of a circle = 14/2 = 7 cm. 8. Given a circle with centre O and radius 2.5 cm, what is the length of the longest chord of the circle. Solution: We know that the diameter of a circle is its longest chord which is twice its radius. So the length of the longest chord of the circle = 2 (2.5) = 5 cm. 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: (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. Page 5 1. Explain the following: (i) Circle (ii) Radius (iii) Centre (iv) Diameter (v) Chord (vi) Interior of a circle. Solution: (i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant. (ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre. (iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points. (iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle. (v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle. (vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a circle. 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: The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre. 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: The figure given below shows a circle with centre O and two perpendicular diameter AC and BD. 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: The figure given below shows the points P, Q and 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. The statements can be written as (i) OQ < 5 cm (ii) OP = 5 cm (iii) OR > 5 cm 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: The figure given below shows the circle with A as centre and a line which passes through B. 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: The figure given below shows a semi-circle with centre O and radius 5 cm. We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts. No, 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. 7. The diameter of a circle is 14 cm, find its radius. Solution: It is given that Diameter of a circle = 14 cm We know that Radius of a circle = Diameter / 2 By substituting the values Radius of a circle = 14/2 = 7 cm. 8. Given a circle with centre O and radius 2.5 cm, what is the length of the longest chord of the circle. Solution: We know that the diameter of a circle is its longest chord which is twice its radius. So the length of the longest chord of the circle = 2 (2.5) = 5 cm. 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: (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. 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: (i) True. (ii) False. (iii) False. (iv) False. (v) True. (vi) True. (vii) False. (viii) False. (ix) True.Read More

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