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

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Question: If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?

Options:

Correct Answer: Angle ACB is equal to angle APB

Solution:

The angles subtended by the same arc at the circumference are equal, hence angle ACB = angle APB.

If two circles intersect at points A and B, which of the following statements is true regarding the angles formed?

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.

Angles Subtended by Arcs – The angles subtended by the same arc at the circumference of a circle are equal.
Circle Intersection – Understanding the properties of angles formed by intersecting circles and their arcs.