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If two circles intersect at points A and B, and the line segment AB is the commo

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Question: If two circles intersect at points A and B, and the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?

Options:

  1. It bisects AB
  2. It is equal to AB
  3. It is longer than AB
  4. It is shorter than AB

Correct Answer: It bisects AB

Solution: 

The perpendicular from the center of a circle to a chord bisects the chord.

If two circles intersect at points A and B, and the line segment AB is the commo

Practice Questions

Q1
If two circles intersect at points A and B, and the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?
  1. It bisects AB
  2. It is equal to AB
  3. It is longer than AB
  4. It is shorter than AB

Questions & Step-by-Step Solutions

If two circles intersect at points A and B, and the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?
  • Step 1: Understand that two circles can intersect at two points, which we call A and B.
  • Step 2: Recognize that the line segment connecting points A and B is called the common chord.
  • Step 3: Identify the center of one of the circles, which we will call O.
  • Step 4: Draw a line from the center O to the chord AB, making sure this line is perpendicular to AB.
  • Step 5: Know that when a line from the center of a circle is perpendicular to a chord, it divides the chord into two equal parts.
  • Step 6: Conclude that the perpendicular line from the center O to the chord AB bisects the chord, meaning it cuts AB into two equal segments.
  • Properties of Chords – The perpendicular from the center of a circle to a chord bisects the chord, which is a fundamental property in circle geometry.
  • Circle Intersection – Understanding how two circles can intersect and the geometric properties that arise from their intersection.
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