If two circles intersect at points A and B, which of the following statements is

Practice Questions

Q1
If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?
  1. Angle AOB is equal to angle ACB
  2. Angle AOB is equal to angle APB
  3. Angle ACB is equal to angle APB
  4. Angle AOB is equal to angle APB + angle ACB

Questions & Step-by-Step Solutions

If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?
  • Step 1: Understand that two circles can intersect at two points, which we will call A and B.
  • Step 2: Identify points C and P on the circumference of the circles such that angle ACB and angle APB are formed.
  • Step 3: Recognize that both angles ACB and APB are subtended by the same arc AB (the arc between points A and B).
  • Step 4: Recall the property of circles: angles subtended by the same arc at the circumference are equal.
  • Step 5: Conclude that since both angles ACB and APB are subtended by arc AB, they must be equal.
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