Are there circles of all possible radii passing through A and B? What is the radius of the smallest Class 9

Are there circles of all possible radii passing through A and B? What is the radius of the smallest Class 9

Question 1.

Are there circles of all possible radii passing through A and B? What is the radius of the smallest circle passing through A and B? What is the radius of the largest circle passing through A and B? Class 9

Answer:

i. No, circles of all possible radii are not possible.

ii. The radius of the smallest circle passing through A and B is half of AB.

iii. There is no largest circle. As the centre moves farther away from AB along the perpendicular bisector, the radius keeps increasing without any limits.

Question 2.

As you move away from segment AB along its perpendicular bisector, do the radii of the circles containing A and B increase or decrease? Class 9

Answer:

As we move away from segment AB along its perpendicular bisector, the radii of the circles containing A and B increase.

Question 3.

As you go along the perpendicular bisector, will the circle drawn from that point through A and B appear more curved or less curved? Class 9

Answer:

As we go along the perpendicular bisector, the circle will appear less curved because a larger circle has a gentler curve.