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Two circles intersect at points A and B. If the radius of the first circle is 5

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Question: Two circles intersect at points A and B. If the radius of the first circle is 5 cm and the second is 3 cm, what is the maximum distance between the centers of the circles?

Options:

  1. 8 cm
  2. 10 cm
  3. 6 cm
  4. 7 cm

Correct Answer: 8 cm

Solution: 

Maximum distance = r1 + r2 = 5 + 3 = 8 cm.

Two circles intersect at points A and B. If the radius of the first circle is 5

Practice Questions

Q1
Two circles intersect at points A and B. If the radius of the first circle is 5 cm and the second is 3 cm, what is the maximum distance between the centers of the circles?
  1. 8 cm
  2. 10 cm
  3. 6 cm
  4. 7 cm

Questions & Step-by-Step Solutions

Two circles intersect at points A and B. If the radius of the first circle is 5 cm and the second is 3 cm, what is the maximum distance between the centers of the circles?
  • Step 1: Identify the radius of the first circle, which is 5 cm.
  • Step 2: Identify the radius of the second circle, which is 3 cm.
  • Step 3: Understand that the maximum distance between the centers of the two circles occurs when they are farthest apart, which is when you add their radii together.
  • Step 4: Add the radius of the first circle (5 cm) to the radius of the second circle (3 cm).
  • Step 5: Calculate the sum: 5 cm + 3 cm = 8 cm.
  • Step 6: Conclude that the maximum distance between the centers of the circles is 8 cm.
  • Circle Geometry – Understanding the properties of circles, particularly the relationship between the radius and the distance between centers.
  • Intersection of Circles – Knowledge of how two circles can intersect and the implications for their centers' distance.
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