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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 angles subtended by AB at the centers of the circles?

Options:

  1. They are equal
  2. They are supplementary
  3. They are complementary
  4. They are unequal

Correct Answer: They are equal

Solution: 

The angles subtended by the common chord AB at the centers of the circles are equal.

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 angles subtended by AB at the centers of the circles?
  1. They are equal
  2. They are supplementary
  3. They are complementary
  4. They are unequal

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 angles subtended by AB at the centers of the circles?
  • 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 centers of the two circles, which we will call O1 for the first circle and O2 for the second circle.
  • Step 4: Notice that the angles subtended by the chord AB at the centers O1 and O2 are the angles formed by the lines O1A and O1B for the first circle, and O2A and O2B for the second circle.
  • Step 5: Use the property of circles that states that the angles subtended by the same chord at the center of the circles are equal.
  • Step 6: Conclude that the angle O1AB is equal to the angle O2AB.
  • Circle Geometry – Understanding the properties of circles, particularly how angles subtended by chords relate to each other.
  • Angles at the Center – The concept that angles subtended by the same chord at the center of a circle are equal.
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