Question

15.
CIRCLES
, A line segment AB is of length 5 cm Draw a circle of radius 4cm passing through A and B.
Can you draw a circle of radius 2 cm passing through
A and B. Give reasons to support your answer.​

Answer 1

Answer:

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Step-by-step explanation:

(1) Draw AB = 5cm

(2) Now, AB as base, construct an isosceles triangle OAB, in which OA = OB = 4cm.

(3) So O will be the centre of the required circle, which passes through A & B.

No! We can not draw a circle with radius 2 cm passing through A & B. As radius OA is hypotenuse of right triangle OAM( M is the mid point of AB) , So, OA > AB/2 . And also OA can be = AB/2

AB = 5 cm

So, AB/2 = 2.5 cm

Hence, the least radius = 2.5 cm, the circle of which can pass through A& B

Answer 2

Steps and reason shown below.

Step-by-step explanation:

Here, AB = 5 cm.

Steps of construction:

(i) Draw a line segment AB of 5 cm.  

(ii) Draw the perpendicular bisectors of AB.  

(iii) Draw an arc which intersects the perpendicular bisectors at point O will be required center.  

(iv) So using center O and radius OA, we will draw a circle. We are unable to draw, we cannot draw a circle with radius 2 cm passing through A and B because when we are drawing an arc of radius 2 cm to center A, the arc will not allow the perpendicular bisector and we will not find the center.