MathematicsState whether true or false:A line segment AB is 5cm in length. Draw a circle of radius 4 cm passing through A and B. Hence, we can draw a circle of radius 2 cm passing through A and B.

State whether true or false:


A line segment AB is 5cm in length. Draw a circle of radius 4 cm passing through A and B. Hence, we can draw a circle of radius 2 cm passing through A and B.


  1. A
    True
  2. B
    False 

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    Solution:

    It is given that AB=5cm and a circle of radius 4 cm passes through points A and B.
    Steps of Construction:
    (i) Draw a line segment AB=5 cm.
    (ii) Draw a perpendicular bisector of AB.
    (iii) With center A and radius 4 cm, draw an arc which intersects the perpendicular bisector at O.
    (iv) With center O and radius OA draw a circle.
    No, we cannot draw a circle of radius 2 cm passing through A and B because when we draw an arc of radius 2 cm with center A, the arc will not intersect the perpendicular bisector and we will not find the center.
    i.e., 2+2=4 cm is shorter than 5 cm.
    Hence, the given statement is false.
    A line segment AB is 5cm in length. Draw a circle of radius 4 cm passing through A and B. Hence, we cannot draw a circle of radius 2 cm passing through A and B.
    Therefore, the correct option is (2).
     
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