Two circles intersect at points A and B. What is the relationship between the an
Practice Questions
Q1
Two circles intersect at points A and B. What is the relationship between the angles ∠AOB and ∠APB, where O is the center of one circle and P is the center of the other?
∠AOB = ∠APB
∠AOB = 2∠APB
∠AOB = ½∠APB
∠AOB + ∠APB = 180 degrees
Questions & Step-by-Step Solutions
Two circles intersect at points A and B. What is the relationship between the angles ∠AOB and ∠APB, where O is the center of one circle and P is the center of the other?
Step 1: Identify the two circles and their centers. Let's call the center of the first circle O and the center of the second circle P.
Step 2: Locate the points where the two circles intersect. These points are A and B.
Step 3: Understand that ∠AOB is the angle formed at the center O of the first circle, with points A and B on the circumference.
Step 4: Recognize that ∠APB is the angle formed at the center P of the second circle, with points A and B also on its circumference.
Step 5: Apply the inscribed angle theorem, which states that the angle at the center of a circle (like ∠AOB) is always twice the angle at the circumference (like ∠APB).
Step 6: Conclude that ∠AOB is equal to 2 times ∠APB.
