Question 13 of 50beginner💡 UnderstandVery Short1 mark

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

Correct Answer

Half the length of AB

Exercise: Exercise Set 5.1 | Q: 4 | (Page 7)
For More Understanding

Explanation

The textbook explains that the centres of all circles passing through two points A and B lie on the perpendicular bisector of the line segment AB. The closest point on this perpendicular bisector to the segment AB is its midpoint. When the midpoint of AB is chosen as the centre, AB becomes the diameter of the circle, and the radius is half the length of AB. As the centre moves away from the midpoint along the perpendicular bisector, the radius increases, making this the least possible radius.

Solution Steps

  1. Step 1: Recognize that the centre of any circle passing through points A and B must lie on the perpendicular bisector of segment AB.

  2. Step 2: Identify that the point on the perpendicular bisector closest to A and B is the midpoint of segment AB.

  3. Step 3: Conclude that with the midpoint as the centre, AB acts as a diameter, making the least possible radius half the length of AB.

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