NCERT Solutions for class 6 
                                            Mathematics 
                                 Chapter 14-Practical Geometry 
                                                     
             Exercise 14.1 
             1. Draw a circle of radius 3.2 cm. 
             Ans : Steps of construction are as follows. 
             A.    Take a compass and measure the length of 3.2cm using ruler scale. 
             B.    Mark a point O which is the centre of the circle we are going to draw. 
             C.    Now place the pointer of the compass at a point O and draw the circle by 
              rotating the compass slowly. 
                                         
              
             2. With the same centre O, draw two circles of radii 4 cm and 2.5 cm. 
             Ans : Steps of construction are as follows. 
             A.    Mark a point O which is the centre of the circle. 
             B.    Now take a compass and measure the length 4cm using scale which is the 
              radius of the first  circle. 
             C.    Now place the pointer of the compass at a point O and draw the first 
              circle slowly. 
             D.    Now take a compass and measure the length of 2.5 cm using scale which 
              is the radius of the second circle. 
             E.    Now place the pointer of the compass at point O and draw the circle 
              slowly. 
             Class VI Maths                 www.vedantu.com                               1 
              
                                                                                                       
                                                       
               
              3. Draw a circle and any two of its diameters. If you join the ends of these 
                diameters, what is the figure obtained if the diameters are perpendicular 
                to each other? How do you check your answer? 
              Ans : If we join the ends of the diameters of the circle, we’ll get a rectangle, 
                because we know that the two chords make 90at the circumference. 
                                         
               ABCD90 
              If the diameters of the circle are perpendicular to each other, then by joining the 
                ends of the diameter we’ll get a square. 
                                             
              As we know that ABCD90, then by measuring we get 
                ABBCCDDA. 
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               All the sides are equal. So ABCD is a square. 
                
               4. Draw any circle and mark points A, B and C such that:  
               (a)     A is on the circle.  
               (b)     B is in the interior of the circle.  
               (c)     C is in the exterior of the circle 
               Ans : 
                                                        
               Steps of construction: 
               (a)     Take a compass and measure any length as a radii of the circle. 
               (b)     Now mark a point O which is the centre of the circle. 
               (c)     Place the pointer of the compass at O and draw the circle slowly. 
               (d)     Now mark a point A which is lying in the circumference of the circle. 
               (e)     Mark any point inside the circle which is point B. 
               (f)     Mark any point outside the circle which is point C. 
                
               5. Let A, B be the centres of two circles of equal radii, draw them so that 
                 each one of them passes through the centre of the other. Let them 
                 intersect at C and D. Examine whether AB and CD are at right angles. 
               Ans: Draw two circles of equal radius. Let A,B be the centre of the two circles. 
               Now, it is given that the radii of each one of the circles pass through the centre 
                 of the other. 
               It is also given that two circles intersect each other at C and D. 
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              We know that the radii of the circle bisect perpendicularly the chord of the 
               circle i.e. Radii is the perpendicular bisector of the chord of the circle. 
                             
                  BOC 90
              So,            . Thus, AB and CD are at right angles. 
                                                        
               
               
               
               
              Class VI Maths                   www.vedantu.com                                  4