What is the least possible radius of a circle through two points A and B? Class 9

What is the least possible radius of a circle through two points A and B? Class 9

Question 1.

What is the least possible radius of a circle through two points A and B? Class 9

Solution:

Since the circle passes through A and B, AB is the diameter.

∴ Least possible radius of the circle = $\frac{\text { radius }}{2}=\frac{\mathrm{AB}}{2}$

Question 2.

A, B and C are three collinear points. Can you find a point P such that PA = PB = PC? What can you say about the perpendicular bisectors of AB and BC? Draw and check. Can you show that for three collinear points A, B and C, the perpendicular bisector of AB and BC are parallel? Is it possible for a circle to pass through collinear points? Can you draw a line that cuts a given circle in three distinct points? Class 9

Answer:

i. For three collinear points A, B and C, there is no point P such that PA = PB = PC.

ii. The perpendicular bisectors of AB and BC are parallel to each other.

iii. Since MN and PQ are the perpendicular bisectors of AB and BC

∴ ∠NMA = ∠QPB = 90°

We know that when the corresponding angles formed by a transversal on a pair of lines are equal to each other, then the pair of lines are parallel to each other. Hence, the perpendicular bisectors of AB and BC are parallel.

iv. No, it not possible for a circle to pass through collinear points.

v. No, we cannot draw a line that cuts a given circle in three distinct points.