Page 1 Points to Remember : Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle. All the radii of a circle are equal. Diameter of a circle A line segment passing through the centre of circle and having its end points on the circle is diameter of the circle. Diameter = 2 × radius Chord of a circle. A line segment with its end points lying on a circle is called the chord of the circle. Secent of a Circle. A line passing through a circle and intersecting the circle at two points is called a secent of the circle. Circumference of a circle. The perimeter of a circle is called the circumference of the circle Semi-circle. The end points of a diameter of a circle divide the circle into two parts ; each part is called a semi-circle. Arc. Any part of a circle is called an arc of the circe. Segments of a Circle A chord AB of a circle divides the circular region into two parts. Each part is called a segment of the circle. The segment containing the centre of the circle is called the major segment, while the segment not containing the centre is called the minor segment of the circle. Sector of a Circle. The area bounded by an arc and the two radii joining the end points of the arc with the centre, is called a sector. If the sector is formed by a major arc then it is called a major sector. If the sector is formed by a minor arc, it is called a minor sector. Concentric circles. Two or more circles with the same centre are called concentric circles. Page 2 Points to Remember : Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle. All the radii of a circle are equal. Diameter of a circle A line segment passing through the centre of circle and having its end points on the circle is diameter of the circle. Diameter = 2 × radius Chord of a circle. A line segment with its end points lying on a circle is called the chord of the circle. Secent of a Circle. A line passing through a circle and intersecting the circle at two points is called a secent of the circle. Circumference of a circle. The perimeter of a circle is called the circumference of the circle Semi-circle. The end points of a diameter of a circle divide the circle into two parts ; each part is called a semi-circle. Arc. Any part of a circle is called an arc of the circe. Segments of a Circle A chord AB of a circle divides the circular region into two parts. Each part is called a segment of the circle. The segment containing the centre of the circle is called the major segment, while the segment not containing the centre is called the minor segment of the circle. Sector of a Circle. The area bounded by an arc and the two radii joining the end points of the arc with the centre, is called a sector. If the sector is formed by a major arc then it is called a major sector. If the sector is formed by a minor arc, it is called a minor sector. Concentric circles. Two or more circles with the same centre are called concentric circles. Q. 1. Take a point O on your note book and draw circles of radii 4 cm., 5.3 cm. and 6.2 cm., each having the same centre. Sol. Method : Take a point O on the paper as shown in the figure. With the help of the rular, open out compasses in such a way that the distance between the metal point and pencil point is 4 cm. Take the compasses in the same position and put its metal point at O and draw the circle. Remove the compasses and again open out the compasses in such a way that the distance between the metal point and pencil point is 5.3 cm. Taking O as the centre, draw another circle. Again remove the compasses and similarly draw the third circle with radius 6.2 cm. Then the required circles are as shown in the figure which have radius OA = 4 cm., OB = 5.3 cm. and OC = 6.2 cm. Q. 2. Draw a circle with centre C and radius 4.5 cm. Mark points P, Q and R such that P lies in the interior of the circle, Q lies on the circle and R lies in the exterior of the circle. Sol. Method : Take a point C on the paper. With the help of the rular, open out the compasses in such a way that the distance between its metal point and pencil point is 4.5 cm. Take the compasses in the same position and put its metal point at C and draw the circle. Mark points P, Q and R as shown in the figure as required. Q. 3. Draw a circle, with centre O and radius 4 cm. Draw a chord AB of the circle. Indicate by marking point X and Y, the minor are AX B and the major are AYB. Sol. Method : Take a point O on the paper. With the help of the rular, open out the compasses in such a way that the distance between the metal point and pencil point is 4 cm. Take the compasses in the same position and put the metal point at O and draw the circle. Take A and B any points on the circle and join AB. Then AB is the chord of the Page 3 Points to Remember : Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle. All the radii of a circle are equal. Diameter of a circle A line segment passing through the centre of circle and having its end points on the circle is diameter of the circle. Diameter = 2 × radius Chord of a circle. A line segment with its end points lying on a circle is called the chord of the circle. Secent of a Circle. A line passing through a circle and intersecting the circle at two points is called a secent of the circle. Circumference of a circle. The perimeter of a circle is called the circumference of the circle Semi-circle. The end points of a diameter of a circle divide the circle into two parts ; each part is called a semi-circle. Arc. Any part of a circle is called an arc of the circe. Segments of a Circle A chord AB of a circle divides the circular region into two parts. Each part is called a segment of the circle. The segment containing the centre of the circle is called the major segment, while the segment not containing the centre is called the minor segment of the circle. Sector of a Circle. The area bounded by an arc and the two radii joining the end points of the arc with the centre, is called a sector. If the sector is formed by a major arc then it is called a major sector. If the sector is formed by a minor arc, it is called a minor sector. Concentric circles. Two or more circles with the same centre are called concentric circles. Q. 1. Take a point O on your note book and draw circles of radii 4 cm., 5.3 cm. and 6.2 cm., each having the same centre. Sol. Method : Take a point O on the paper as shown in the figure. With the help of the rular, open out compasses in such a way that the distance between the metal point and pencil point is 4 cm. Take the compasses in the same position and put its metal point at O and draw the circle. Remove the compasses and again open out the compasses in such a way that the distance between the metal point and pencil point is 5.3 cm. Taking O as the centre, draw another circle. Again remove the compasses and similarly draw the third circle with radius 6.2 cm. Then the required circles are as shown in the figure which have radius OA = 4 cm., OB = 5.3 cm. and OC = 6.2 cm. Q. 2. Draw a circle with centre C and radius 4.5 cm. Mark points P, Q and R such that P lies in the interior of the circle, Q lies on the circle and R lies in the exterior of the circle. Sol. Method : Take a point C on the paper. With the help of the rular, open out the compasses in such a way that the distance between its metal point and pencil point is 4.5 cm. Take the compasses in the same position and put its metal point at C and draw the circle. Mark points P, Q and R as shown in the figure as required. Q. 3. Draw a circle, with centre O and radius 4 cm. Draw a chord AB of the circle. Indicate by marking point X and Y, the minor are AX B and the major are AYB. Sol. Method : Take a point O on the paper. With the help of the rular, open out the compasses in such a way that the distance between the metal point and pencil point is 4 cm. Take the compasses in the same position and put the metal point at O and draw the circle. Take A and B any points on the circle and join AB. Then AB is the chord of the circle. Mark points X and Y on the circle as shown. Then arc AXB and arc AYB are the required minor and major arcs respectvely. Q. 4. Which of the following statements are true and which are false ? (i) Each radius of a circle is also a chord of the circle. (ii) Each diameter of a circle is also a chord of the circle. (iii) The centre of a circle bisects each chord of the circle. (iv) Secent of a circle is a segment having its end points on the circle. (v) Chord of a circle is a segment having its end points on the circle. Sol. (i) False (ii) True (iii) False (iv) False (v) True. Q. 5. Draw a circle with centre O and radius 3·7 cm. Draw a sector having the angle 72º. Sol. Steps of construction : (i) With centre O and radius 3·7 cm, draw a circle. (ii) Take a point A on the circumference of the circle. (iii) Join OA. (iv) At O, draw another radius OB such that AOB = 72º with the help of protractor. Then sector AOB is the required one. Q. 6. Fill in the blanks by using <, >, = or (i) OP........OQ, where O is the centre of the circle, P lies on the circle and Q is in the interior of the circle. (ii) OP........OR, where O is the centre of the circle, P lies on the circle and R lies in the exterior of the circle. (iii) Major arc..........minor arc of the circle. (iv) Major arc........semicircumference of the circle. Sol. (i) > (ii) < (iii) > (iv) >. Ans. Q. 7. Fill in the blanks : (i) A diameter of a circle is a chord that..........the centre. (ii) A radius of a circle is a line segment with one end point.........and the other end point......... . (iii) If we join any two points of a circle by a line segment, we obtain a..........of the circle. (iv) Any part of a circle is called an...........of the circle. (v) The figure bounded by an arc and the two radii joining the end points of the arc with the centre is called a...........of the circle. Sol. (i) Passes through (ii) at the centre, on the circle (iii) chord (iv) arc (v) sector. Ans.Read More

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