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If two circles intersect at points A and B, and the distance between their cente

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Question: If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)

Options:

  1. 5 cm
  2. 10 cm
  3. 15 cm
  4. 20 cm

Correct Answer: 10 cm

Exam Year: 2021

Solution: 

The maximum radius of each circle can be half the distance between the centers, which is 10 cm.

If two circles intersect at points A and B, and the distance between their cente

Practice Questions

Q1
If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
  1. 5 cm
  2. 10 cm
  3. 15 cm
  4. 20 cm

Questions & Step-by-Step Solutions

If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
  • Step 1: Understand that two circles can intersect at two points, A and B.
  • Step 2: Identify that the distance between the centers of the two circles is given as 10 cm.
  • Step 3: Realize that for the circles to intersect, the radius of each circle must be less than or equal to half the distance between the centers.
  • Step 4: Calculate half of the distance between the centers: 10 cm / 2 = 5 cm.
  • Step 5: Conclude that the maximum possible radius of each circle is 5 cm.
  • Circle Intersection – Understanding the geometric properties of intersecting circles, particularly the relationship between the distance between their centers and their radii.
  • Radius Calculation – Calculating the maximum radius of circles based on their center distance and intersection points.
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