Question

A line segment AB is length 5 cm. Draw a circle of radius 4 cm passing through A and B. Can you draw a circle of radius 2 cm passing through A and B? Give reason in support of your answer.

Answer 1

we can not draw a circle of radius 2 cm passing thought A & B if AB = 5 cm

Step-by-step explanation:

A line segment AB is length 5 cm

We need to  Draw a circle of radius 4 cm passing through A and B

=> AB is a chord

Maximum chord length = Diameter = 2 * radius

=> minimum radius = 5/2 = 2.5 cm

hence we can not draw a circle of radius 2 cm passing thought A & B

Construction:

Step1 : Draw a line segment AB = 5 cm

Step 2 : Using compass width slightly less than AB and taking A as center draw arcs on both sides of AB

Step 3 : keeping Compass width same , now taking B as center draw arc , intersecting arcs drawn earlier at C & D

Step 4 : draw a line passing through C & D

Step 5 : taking compass width = 4 cm & taking A or B as center draw an arc intersecting line drawn in step 4 at O

Step 6 : now taking O as center & compass width = 4 cm , draw a circle passing though  A & B

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Answer 2

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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